This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—$100 = 10 \times 10$. The key relationship: $\frac{1}{10} = \frac{10}{100}$ (one tenth equals ten hundredths), so any fraction $\frac{a}{10} = \frac{10a}{100}$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $\frac{10a}{100} + \frac{b}{100} = \frac{10a + b}{100}$. Convert $8/10$ to hundredths and add $9/100$: $\frac{8}{10} = \frac{8 \times 10}{100} = \frac{80}{100}$. Then add: $\frac{80}{100} + \frac{9}{100} = \frac{80 + 9}{100} = \frac{89}{100}$. Choice A is correct because converting $8/10$: multiply numerator $8 \times 10 = 80$, denominator $10 \times 10 = 100$, giving $\frac{80}{100}$; then adding: $\frac{80}{100} + \frac{9}{100}$, add numerators: $80 + 9 = 89$, keep denominator 100: $\frac{89}{100}$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added $8+9=17$ directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid ($10\times10$ squares)—each COLUMN is $\frac{1}{10} = 10$ squares, each SQUARE is $\frac{1}{100}$. To convert tenths to hundredths, multiply numerator by 10: $\frac{8}{10} = \frac{8\times10}{100} = \frac{80}{100}$. Check: count squares ($80$ squares for 8 columns). Then add: $\frac{80}{100} + \frac{9}{100} = \frac{89}{100}$ ($80 + 9 = 89$ squares total). Connect to decimals: $\frac{8}{10} = 0.8$, $\frac{9}{100} = 0.09$, $0.8 + 0.09 = 0.89 = \frac{89}{100}$. Use money: 8 dimes ($\frac{8}{10}$ dollar) = 80 pennies ($\frac{80}{100}$ dollar), plus 9 pennies = 89 pennies = $\frac{89}{100}$ dollar. Pattern: $\frac{1}{10}=\frac{10}{100}$, $\frac{2}{10}=\frac{20}{100}$, $\frac{8}{10}=\frac{80}{100}$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—100 is the common denominator since $100 = 10 \times 10$. The key relationship: $1/10 = 10/100$ (one tenth equals ten hundredths), so any fraction $a/10 = (10a)/100$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $(10a)/100 + b/100 = (10a + b)/100$. To add $1/10 + 25/100$, first convert $1/10$ to hundredths: $1/10 = (1 \times 10)/100 = 10/100$. Then add: $10/100 + 25/100 = (10 + 25)/100 = 35/100$. Choice C is correct because converting $1/10$: multiply numerator $1 \times 10 = 10$, denominator $10 \times 10 = 100$, giving $10/100$; then adding: $10/100 + 25/100$, add numerators: $10 + 25 = 35$, keep denominator 100: $35/100$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice A represents an arithmetic error (added $1 + 25=26$ without converting), which happens when students make calculation mistake or don't convert. To help students: Visualize with hundredths grid ($10\times10$ squares)—each column is $1/10 = 10$ squares, each square is $1/100$. To convert tenths to hundredths, multiply numerator by 10: $1/10 = (1\times10)/100 = 10/100$. Check: count squares ($10$ squares for 1 column). Then add: $10/100 + 25/100 = 35/100$ ($10 + 25 = 35$ squares total). Connect to decimals: $1/10 = 0.1$, $25/100 = 0.25$, $0.1 + 0.25 = 0.35 = 35/100$. Use money: 1 dime ($1/10$ dollar) = 10 pennies ($10/100$ dollar), plus 25 pennies = 35 pennies = $35/100$ dollar. Pattern: $1/10=10/100$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—100 is the common denominator since 100 = 10 × 10. The key relationship: 1/10 = 10/100 (one tenth equals ten hundredths), so any fraction a/10 = (10a)/100 by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: (10a)/100 + b/100 = (10a + b)/100. To add 5/10 + 23/100, first convert 5/10 to hundredths: 5/10 = (5 × 10)/100 = 50/100. Then add: 50/100 + 23/100 = (50 + 23)/100 = 73/100. Choice B is correct because converting 5/10: multiply numerator 5 × 10 = 50, denominator 10 × 10 = 100, giving 50/100; then adding: 50/100 + 23/100, add numerators: 50 + 23 = 73, keep denominator 100: 73/100. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice A represents an arithmetic error (added 5 + 23=28 without converting), which happens when students make calculation mistake or don't convert. To help students: Visualize with hundredths grid (10×10 squares)—each column is 1/10 = 10 squares, each square is 1/100. To convert tenths to hundredths, multiply numerator by 10: 5/10 = (5×10)/100 = 50/100. Check: count squares (50 squares for 5 columns). Then add: 50/100 + 23/100 = 73/100 (50 + 23 = 73 squares total). Connect to decimals: 5/10 = 0.5, 23/100 = 0.23, 0.5 + 0.23 = 0.73 = 73/100. Use money: 5 dimes (5/10 dollar) = 50 pennies (50/100 dollar), plus 23 pennies = 73 pennies = 73/100 dollar. Pattern: 1/10=10/100, 2/10=20/100, 5/10=50/100 (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—100 is the common denominator since $100 = 10 \times 10$. The key relationship: $1/10 = 10/100$ (one tenth equals ten hundredths), so any fraction $a/10 = (10a)/100$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $(10a)/100 + b/100 = (10a + b)/100$. To add $7/10 + 6/100$, first convert $7/10$ to hundredths: $7/10 = (7 \times 10)/100 = 70/100$. Then add: $70/100 + 6/100 = (70 + 6)/100 = 76/100$. Choice C is correct because converting $7/10$: multiply numerator $7 \times 10 = 70$, denominator $10 \times 10 = 100$, giving $70/100$; then adding: $70/100 + 6/100$, add numerators: $70 + 6 = 76$, keep denominator 100: $76/100$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice A represents adding without converting (added $7+6=13$ directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid ($10\times10$ squares)—each column is $1/10 = 10$ squares, each square is $1/100$. To convert tenths to hundredths, multiply numerator by 10: $7/10 = (7\times10)/100 = 70/100$. Check: count squares ($70$ squares for 7 columns). Then add: $70/100 + 6/100 = 76/100$ ($70 + 6 = 76$ squares total). Connect to decimals: $7/10 = 0.7$, $6/100 = 0.06$, $0.7 + 0.06 = 0.76 = 76/100$. Use money: 7 dimes ($7/10$ dollar) = 70 pennies ($70/100$ dollar), plus 6 pennies = 76 pennies = $76/100$ dollar. Pattern: $1/10=10/100$, $2/10=20/100$, $7/10=70/100$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—$100$ is the common denominator since $100 = 10 \times 10$. The key relationship: $\frac{1}{10} = \frac{10}{100}$ (one tenth equals ten hundredths), so any fraction $\frac{a}{10} = \frac{10a}{100}$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $\frac{10a}{100} + \frac{b}{100} = \frac{10a + b}{100}$. To add $\frac{4}{10} + \frac{27}{100}$, first convert $\frac{4}{10}$ to hundredths: $\frac{4}{10} = \frac{4 \times 10}{100} = \frac{40}{100}$. Then add: $\frac{40}{100} + \frac{27}{100} = \frac{40 + 27}{100} = \frac{67}{100}$. You can also think decimally: $\frac{4}{10} = 0.4$, $\frac{27}{100} = 0.27$, sum = $0.67$. Choice A is correct because converting $\frac{4}{10}$: multiply numerator $4 \times 10 = 40$, denominator $10 \times 10 = 100$, giving $\frac{40}{100}$; then adding: $\frac{40}{100} + \frac{27}{100}$, add numerators: $40 + 27 = 67$, keep denominator 100: $\frac{67}{100}$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added $4+27=31$, but mismatched), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid (10×10 squares)—each COLUMN is $\frac{1}{10} = 10$ squares, each SQUARE is $\frac{1}{100}$. To convert tenths to hundredths, multiply numerator by 10: $\frac{4}{10} = \frac{4 \times 10}{100} = \frac{40}{100}$. Check: count squares ($40$ squares for 4 columns). Then add: $\frac{40}{100} + \frac{27}{100} = \frac{67}{100}$ ($40 + 27 = 67$ squares total). Connect to decimals: $\frac{4}{10} = 0.4$ (four tenths), $\frac{27}{100} = 0.27$ (twenty-seven hundredths), $0.4 + 0.27 = 0.67$ (sixty-seven hundredths) = $\frac{67}{100}$. Use money: 4 dimes ($\frac{4}{10}$ dollar) = 40 pennies ($\frac{40}{100}$ dollar), plus 27 pennies = 67 pennies = $\frac{67}{100}$ dollar. Pattern: $\frac{1}{10}=\frac{10}{100}$, $\frac{2}{10}=\frac{20}{100}$, $\frac{4}{10}=\frac{40}{100}$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—100 is the common denominator since 100 = 10 × 10. The key relationship: 1/10 = 10/100 (one tenth equals ten hundredths), so any fraction a/10 = (10a)/100 by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: (10a)/100 + b/100 = (10a + b)/100. To add 9/10 + 3/100, first convert 9/10 to hundredths: 9/10 = (9 × 10)/100 = 90/100. Then add: 90/100 + 3/100 = (90 + 3)/100 = 93/100. Choice A is correct because converting 9/10: multiply numerator 9 × 10 = 90, denominator 10 × 10 = 100, giving 90/100; then adding: 90/100 + 3/100, add numerators: 90 + 3 = 93, keep denominator 100: 93/100. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added 9+3=12 directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid (10×10 squares)—each column is 1/10 = 10 squares, each square is 1/100. To convert tenths to hundredths, multiply numerator by 10: 9/10 = (9×10)/100 = 90/100. Check: count squares (90 squares for 9 columns). Then add: 90/100 + 3/100 = 93/100 (90 + 3 = 93 squares total). Connect to decimals: 9/10 = 0.9, 3/100 = 0.03, 0.9 + 0.03 = 0.93 = 93/100. Use money: 9 dimes (9/10 dollar) = 90 pennies (90/100 dollar), plus 3 pennies = 93 pennies = 93/100 dollar. Pattern: 1/10=10/100, 2/10=20/100, 9/10=90/100 (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—100 is the common denominator since $100 = 10 \times 10$. The key relationship: $1/10 = 10/100$ (one tenth equals ten hundredths), so any fraction $a/10 = (10a)/100$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $(10a)/100 + b/100 = (10a + b)/100$. To add $9/10 + 4/100$, first convert $9/10$ to hundredths: $9/10 = (9 \times 10)/100 = 90/100$. Then add: $90/100 + 4/100 = (90 + 4)/100 = 94/100$. Choice A is correct because converting $9/10$: multiply numerator $9 \times 10 = 90$, denominator $10 \times 10 = 100$, giving $90/100$; then adding: $90/100 + 4/100$, add numerators: $90 + 4 = 94$, keep denominator 100: $94/100$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added $9+4=13$ directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid ($10\times10$ squares)—each COLUMN is $1/10 = 10$ squares, each SQUARE is $1/100$. To convert tenths to hundredths, multiply numerator by 10: $9/10 = (9\times10)/100 = 90/100$. Check: count squares ($90$ squares for $9$ columns). Then add: $90/100 + 4/100 = 94/100$ ($90 + 4 = 94$ squares total). Connect to decimals: $9/10 = 0.9$, $4/100 = 0.04$, $0.9 + 0.04 = 0.94 = 94/100$. Use money: $9$ dimes ($9/10$ dollar) = $90$ pennies ($90/100$ dollar), plus $4$ pennies = $94$ pennies = $94/100$ dollar. Pattern: $1/10=10/100$, $2/10=20/100$, $9/10=90/100$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—100 is the common denominator since 100 = 10 × 10. The key relationship: $1/10 = 10/100$ (one tenth equals ten hundredths), so any fraction $a/10 = (10a)/100$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $(10a)/100 + b/100 = (10a + b)/100$. To add $6/10 + 9/100$, first convert $6/10$ to hundredths: $6/10 = (6 × 10)/100 = 60/100$. Then add: $60/100 + 9/100 = (60 + 9)/100 = 69/100$. Choice A is correct because converting $6/10$: multiply numerator 6 × 10 = 60, denominator 10 × 10 = 100, giving $60/100$; then adding: $60/100 + 9/100$, add numerators: 60 + 9 = 69, keep denominator 100: $69/100$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added 6+9=15 directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid (10×10 squares)—each column is $1/10 = 10$ squares, each square is $1/100$. To convert tenths to hundredths, multiply numerator by 10: $6/10 = (6×10)/100 = 60/100$. Check: count squares (60 squares for 6 columns). Then add: $60/100 + 9/100 = 69/100$ (60 + 9 = 69 squares total). Connect to decimals: $6/10 = 0.6$, $9/100 = 0.09$, $0.6 + 0.09 = 0.69 = 69/100$. Use money: 6 dimes ($6/10$ dollar) = 60 pennies ($60/100$ dollar), plus 9 pennies = 69 pennies = $69/100$ dollar. Pattern: $1/10=10/100$, $2/10=20/100$, $6/10=60/100$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—$100 = 10 \times 10$. The key relationship: $\frac{1}{10} = \frac{10}{100}$ (one tenth equals ten hundredths), so any fraction $\frac{a}{10} = \frac{10a}{100}$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $\frac{10a}{100} + \frac{b}{100} = \frac{10a + b}{100}$. To add $\frac{3}{10} + \frac{27}{100}$, first convert $\frac{3}{10}$ to hundredths: $\frac{3}{10} = \frac{3 \times 10}{100} = \frac{30}{100}$. Then add: $\frac{30}{100} + \frac{27}{100} = \frac{30 + 27}{100} = \frac{57}{100}$. Choice A is correct because converting $\frac{3}{10}$: multiply numerator $3 \times 10 = 30$, denominator $10 \times 10 = 100$, giving $\frac{30}{100}$; then adding: $\frac{30}{100} + \frac{27}{100}$, add numerators: $30 + 27 = 57$, keep denominator 100: $\frac{57}{100}$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents the conversion only without adding (stopped at $\frac{30}{100}$), which happens when students don't complete the addition. To help students: Visualize with hundredths grid ($10\times10$ squares)—each COLUMN is $\frac{1}{10} = 10$ squares, each SQUARE is $\frac{1}{100}$. To convert tenths to hundredths, multiply numerator by 10: $\frac{3}{10} = \frac{3\times10}{100} = \frac{30}{100}$. Check: count squares ($30$ squares for $3$ columns). Then add: $\frac{30}{100} + \frac{27}{100} = \frac{57}{100}$ ($30 + 27 = 57$ squares total). Connect to decimals: $\frac{3}{10} = 0.3$, $\frac{27}{100} = 0.27$, $0.3 + 0.27 = 0.57 = \frac{57}{100}$. Use money: $3$ dimes ($\frac{3}{10}$ dollar) = $30$ pennies ($\frac{30}{100}$ dollar), plus $27$ pennies = $57$ pennies = $\frac{57}{100}$ dollar. Pattern: $\frac{1}{10}=\frac{10}{100}$, $\frac{2}{10}=\frac{20}{100}$, $\frac{3}{10}=\frac{30}{100}$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—100 is the common denominator since $100 = 10 \times 10$. The key relationship: $1/10 = 10/100$ (one tenth equals ten hundredths), so any fraction $a/10 = (10a)/100$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $(10a)/100 + b/100 = (10a + b)/100$. Maya walked $7/10$ kilometer and then $12/100$ kilometer more; convert $7/10$ to hundredths: $7/10 = (7 \times 10)/100 = 70/100$. Then add: $70/100 + 12/100 = (70 + 12)/100 = 82/100$. Choice A is correct because converting $7/10$: multiply numerator $7 \times 10 = 70$, denominator $10 \times 10 = 100$, giving $70/100$; then adding: $70/100 + 12/100$, add numerators: $70 + 12 = 82$, keep denominator 100: $82/100$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added $7+12=19$ directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid ($10\times10$ squares)—each COLUMN is $1/10 = 10$ squares, each SQUARE is $1/100$. To convert tenths to hundredths, multiply numerator by 10: $7/10 = (7\times10)/100 = 70/100$. Check: count squares ($70$ squares for 7 columns). Then add: $70/100 + 12/100 = 82/100$ ($70 + 12 = 82$ squares total). Connect to decimals: $7/10 = 0.7$, $12/100 = 0.12$, $0.7 + 0.12 = 0.82 = 82/100$. Use money: 7 dimes ($7/10$ dollar) = 70 pennies ($70/100$ dollar), plus 12 pennies = 82 pennies = $82/100$ dollar. Pattern: $1/10=10/100$, $2/10=20/100$, $7/10=70/100$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.