SSAT Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #1 : Add And Subtract Mixed Numbers With Like Denominators: Ccss.Math.Content.4.Nf.B.3c

Solve: 

\(\displaystyle 6\frac{4}{10}+5\frac{5}{10}\)

Possible Answers:

\(\displaystyle 11\frac{8}{10}\)

\(\displaystyle 11\frac{9}{10}\)

\(\displaystyle 11\frac{4}{5}\)

\(\displaystyle 11\frac{8}{20}\)

\(\displaystyle 11\frac{9}{20}\)

Correct answer:

\(\displaystyle 11\frac{9}{10}\)

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions. 

\(\displaystyle 6+5=11\)

\(\displaystyle \frac{4}{10}+\frac{5}{10}=\frac{9}{10}\)

Remember, when we are adding fractions we must have common denominators and we only add the numerators. 

Example Question #65 : Fractions

On Monday it snowed \(\displaystyle \frac{1}{4}\) of an inch in the afternoon and \(\displaystyle \frac{1}{4}\) of an inch in the evening. What was the total amount of snowfall on Monday?

Possible Answers:

\(\displaystyle \frac{1}{4}\)

\(\displaystyle \frac{2}{4}\)

\(\displaystyle \frac{5}{5}\)

\(\displaystyle \frac{4}{4}\)

\(\displaystyle \frac{3}{4}\)

Correct answer:

\(\displaystyle \frac{2}{4}\)

Explanation:

To solve this problem, we are putting the amount of snowfall from the afternoon and the evening together, so we add the fractions. 

\(\displaystyle \frac{1}{4}+\frac{1}{4}=\frac{2}{4}\)

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Example Question #11 : Understand Decimal Notation For Fractions, And Compare Decimal Fractions

Solve the following:

\(\displaystyle \frac{5}{10}+\frac{2}{100}=\)

Possible Answers:

\(\displaystyle \frac{7}{10}\)

\(\displaystyle \frac{50}{100}\)

\(\displaystyle \frac{7}{100}\)

\(\displaystyle \frac{20}{100}\)

\(\displaystyle \frac{52}{100}\)

Correct answer:

\(\displaystyle \frac{52}{100}\)

Explanation:

When we add fractions, we must have common denominators. Whenever we have a number over \(\displaystyle 10\) or \(\displaystyle 100\) we can add \(\displaystyle 0\)(s) to the numerator and denominator to make common denominators.

\(\displaystyle \frac{5}{10}=\frac{50}{100}\)

\(\displaystyle \frac{50}{100}+\frac{2}{100}=\frac{52}{100}\)

Example Question #3 : Decompose A Fraction Into A Sum Of Fractions: Ccss.Math.Content.4.Nf.B.3b

\(\displaystyle \frac{2}{7}\) is equal to which of the options below? 

Possible Answers:

\(\displaystyle \frac{1}{7}+\frac{1}{7}\)

\(\displaystyle \frac{1}{7}+\frac{1}{7}+\frac{1}{7}\)

\(\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{3}+\frac{1}{4}\)

\(\displaystyle \frac{1}{3}+\frac{1}{4}\)

\(\displaystyle \frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}\)

Correct answer:

\(\displaystyle \frac{1}{7}+\frac{1}{7}\)

Explanation:

When we add fractions, we have to have common denominators and we only add the numerators. 

\(\displaystyle \frac{1}{7}+\frac{1}{7}=\frac{2}{7}\)

Example Question #221 : Build Fractions From Unit Fractions

In Charlie's pantry, \(\displaystyle \frac{2}{5}\) of the items are potato chips, \(\displaystyle \frac{1}{5}\) of the items are tortilla chips, and the rest are cookies or crackers. What fraction are chips?

Possible Answers:

\(\displaystyle \frac{5}{5}\)

\(\displaystyle \frac{3}{5}\)

\(\displaystyle \frac{4}{5}\)

\(\displaystyle \frac{1}{5}\)

\(\displaystyle \frac{2}{5}\)

Correct answer:

\(\displaystyle \frac{3}{5}\)

Explanation:

To solve this problem, we are putting the potato chips and the tortilla chips together, so we add the fractions. 

\(\displaystyle \frac{2}{5}+\frac{1}{5}=\frac{3}{5}\)

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Example Question #1 : How To Subtract Fractions

\(\displaystyle 7 \frac{1}{2}\) hours is how many more minutes than \(\displaystyle 3 \frac{3}{4}\) hours?

Possible Answers:

\(\displaystyle 255\)

\(\displaystyle 225\)

\(\displaystyle 200\)

\(\displaystyle 185\)

\(\displaystyle 245\)

Correct answer:

\(\displaystyle 225\)

Explanation:

This question requires you to subtract fractions as well as convert hours to minutes.  

Subtracting \(\displaystyle 3\frac{3}{4}\) hours \(\displaystyle \left ( \frac{15}{4} \right )\) from \(\displaystyle 7\frac{1}{2}\) hours \(\displaystyle \left ( \frac{15}{2}\ or\ \frac{30}{4} \right )\)

you get \(\displaystyle 3\frac{3}{4}\) hours \(\displaystyle \left ( \frac{15}{4} \right )\).  

3 hours is 180 minutes \(\displaystyle \left ( 3\cdot 60 \right )\)

and \(\displaystyle \frac{3}{4}\) of an hour is 45 minutes \(\displaystyle \left ( \frac{3}{4}\cdot 60 \right )\).

Thus the answer is

\(\displaystyle 180+45=225\ minutes\)

Example Question #1 : How To Subtract Fractions

Evaluate:

\(\displaystyle 9 - 5 \frac{3}{7}\)

Possible Answers:

\(\displaystyle 4 \frac{3}{7}\)

\(\displaystyle 4 \frac{4}{7}\)

\(\displaystyle 3 \frac{3}{7}\)

\(\displaystyle 4 \frac{2}{7}\)

\(\displaystyle 3 \frac{4}{7}\)

Correct answer:

\(\displaystyle 3 \frac{4}{7}\)

Explanation:

"Borrow" 1 from the 9 to form \(\displaystyle 8 \frac{7}{7}\). You can then subtract integers and fractions vertically:

\(\displaystyle 8 \frac{7}{7}\)

\(\displaystyle \underline{5 \frac{3}{7}}\)

\(\displaystyle 3 \frac{4}{7}\)

Example Question #2 : How To Subtract Fractions

Evaluate:

\(\displaystyle 6 \frac{1}{5} - 4 \frac{1}{2}\)

Possible Answers:

\(\displaystyle 2 \frac{3}{10}\)

\(\displaystyle 1 \frac{3}{5}\)

\(\displaystyle 2 \frac{1}{10}\)

\(\displaystyle 1 \frac{7}{10}\)

\(\displaystyle 1 \frac{9}{10}\)

Correct answer:

\(\displaystyle 1 \frac{7}{10}\)

Explanation:

Rewrite as the difference of improper fractions:

\(\displaystyle 6 \frac{1}{5} - 4 \frac{1}{2} = \frac{6 \times 5 + 1}{5} - \frac{4 \times 2 + 1}{2} = \frac{31}{5} - \frac{9}{2}\)

Rewrite with a common denominator, then subtract numerators:

\(\displaystyle \frac{31}{5} - \frac{9}{2} = \frac{2 \times 31}{2 \times 5} - \frac{9\times 5}{2\times 5} = \frac{62}{10} - \frac{45}{10} = \frac{17}{10}\)

Rewrite as a mixed number:

\(\displaystyle 17 \div 10 = 1 \textrm{ R } 7\)

\(\displaystyle \frac{17}{10} = 1 \frac{7}{10}\)

Example Question #3 : How To Subtract Fractions

Evaluate:

\(\displaystyle 8 \frac{4}{5} - 4 \frac{1}{3}\)

Possible Answers:

\(\displaystyle 4 \frac{8}{15 }\)

\(\displaystyle 4 \frac{3}{5 }\)

\(\displaystyle 4 \frac{1}{3 }\)

\(\displaystyle 4 \frac{1}{2 }\)

\(\displaystyle 4 \frac{7}{15 }\)

Correct answer:

\(\displaystyle 4 \frac{7}{15 }\)

Explanation:

Rewrite as the difference of improper fractions:

\(\displaystyle 8 \frac{4}{5} - 4 \frac{1}{3} = \frac{8 \times 5 + 4}{5} - \frac{4 \times 3 + 1}{3} = \frac{44}{5} - \frac{13}{3}\)

Rewrite with a common denominator, then subtract numerators:

\(\displaystyle \frac{44}{5} - \frac{13}{3} = \frac{44\times 3}{5 \times 3} - \frac{5 \times13}{5 \times3} = \frac{132}{15 } - \frac{65}{15 } = \frac{67}{15 }\)

Rewrite as a mixed number:

\(\displaystyle 67\div 15 = 4 \textrm{ R } 7\)

so

\(\displaystyle \frac{67}{15 } = 4 \frac{7}{15 }\)

Example Question #4 : How To Subtract Fractions

Evaluate:

\(\displaystyle 5 - 1 \frac{4}{5}\)

Possible Answers:

\(\displaystyle 3 \frac{1}{5}\)

\(\displaystyle 3 \frac{3}{5}\)

\(\displaystyle 4 \frac{4}{5}\)

\(\displaystyle 4 \frac{1}{5}\)

\(\displaystyle 3 \frac{4}{5}\)

Correct answer:

\(\displaystyle 3 \frac{1}{5}\)

Explanation:

"Borrow" 1 from the 5 to form \(\displaystyle 4 \frac{5}{5}\). You can then subtract integers and fractions vertically:

\(\displaystyle 4 \frac{5}{5}\)

\(\displaystyle \underline{1 \frac{4}{5}}\)

\(\displaystyle 3 \frac{1}{5}\)

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