ISEE Lower Level Quantitative Reasoning - How to find symmetry

Mr. Thomas' rectangular garden has a width of feet. The length of his garden is exactly half the distance of the width of the garden. How long is the length of Mr. Thomas' garden?

$16 \text{ ft}$

$18 \text{ ft}$

$8 \text{ ft}$

$8 \text{ in}$

Explanation

The length of Mr. Thomas' garden is exactly half the distance of the width of the garden.

The width of the garden is feet.

Thus, the length is equal to,

$\frac{32}{2}=16$

In a football contest, Jeff threw the football twice as far as Robby. If Jeff threw the ball $\small 38$ yards, how many yards did Robby throw the ball?

$\small 19 \text{ yds}$

$\small 18 \text{ yds}$

$\small 16$ yards

$\small 24 \text{ yds}$

Explanation

Since Jeff threw the football twice as far as Robby, divide $\small 38$ by $\small 2$ .

$\small 38\div2=19$

Line segment $\small \bar{xy}$ is twice as long as line segment $\small \bar{ab}$ and half as long as line segment $\small \bar{cd}$ . If line segment $\small \bar{cd}$ is $\small 84$ meters, how long is line segment $\small \bar{xy}$ ?

$\small 42 \text{ m}$

$\small 38 \text{ m}$

$\small 44 \text{ m}$

$\small 39 \text{ m}$

Explanation

Since line segment $\small \bar{xy}$ is half the length of line segment $\small \bar{cd}$ we need to divide $\small 84$ by $\small 2$ .

$\small 84\div2=42$

The cable on Ryan's new cellphone charger is twice as long as his old cellphone charger cable. If Ryan's new cellphone charger has a feet long cable, how long was his old charger cable?

${}\small 1\tfrac{1}{2}$

$1\tfrac{3}{4}$

$1\tfrac{1}{4}$

Explanation

To find the length of Ryan's old cellphone cable, divide the length of his new cellphone charger in half.

The solution is:

$\small 3\div2=1\tfrac{1}{2}$

Celeste is Debra's year old daughter. Both Debra and Celeste measured their height on the wall. Celeste was surprised to find out that she is exactly half the height of her mother. If Debra is $5 \tfrac{1}{2}$ feet tall, how tall is Celeste?

$2\tfrac{3}{4} \text{ ft}$

${}\frac{11}{2} \text{ ft}$

$2\tfrac{2}{4} \text{ ft}$

${}2\tfrac{1}{4} \text{ ft}$

Explanation

Debra is $5\tfrac{1}{2}$ feet tall. Celeste is half the height of her mother Debra.

Thus, to find Celeste's height, divide $5\tfrac{1}{2}$ in half.

The solution is:

Step one: convert $5\tfrac{1}{2}$ into an improper fraction.

$5\tfrac{1}{2}=\frac{11}{2}$

Step two: divide $\frac{11}{2}$ by .

$\frac{\frac{11}{2}}{2}=\frac{11}{2}\cdot\frac{1}{2}=\frac{11}{4}$

Step three: express $\frac{11}{4}$ in feet as a mixed number.

$11\div4=2\tfrac{3}{4}$

Line segment $\small \bar{xy}$ goes exactly halfway across a sheet of paper. If the sheet of paper has a width of $\small 12\tfrac{1}{2}$ inches, how long is line segment $\small \bar{xy}$ ?

$\small 6\tfrac{1}{4} \text{ in}$

$\small 6\tfrac{1}{2} \text{ in}$

$\small 6 \text{ in}$

$\small 6\tfrac{3}{4} \text{ in}$

Explanation

Since the length of line segment $\small \bar{xy}$ is half of $\small 12\tfrac{1}{2}$ , convert $\small 12\tfrac{1}{2}$ to a mixed number.

$\small 12\tfrac{1}{2}= \frac{12 \cdot 2 +1}{2}= \frac{25}{2}$

Then divide $\small \frac{25}{2}$ by .

$\small \frac{25}{2}\div2=\frac{25}{2}\times \frac{1}{2}=\frac{25}{4}$

Then convert $\small \frac{25}{4}$ to a mixed number.

$\small \frac{25}{4}=6\tfrac{1}{4}$

Find the midpoint between coordinate points $\small (-2,4)$ and $\small \small (4,4)$ .

$\small (1,4)$

$\small (0,4)$

$\small (0,0)$

$\small (1,0)$

Explanation

To find the midpoint between these two coordinate points, use the formula,

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right )$

Since our and our the midpoint formula becomes,

$\left(\frac{-2+4}{2},\frac{4+4}{2}\right )=\left(\frac{2}{2}, \frac{8}{2} \right )=(1,4)$ .

Ms. Johnson is knitting a blanket for her grandson. She has a piece of yarn that is exactly feet long however, she only needs half of the piece of yarn. What is the length of the piece of yarn that Ms. Johnson needs to make the blanket for her grandson?

$2.5 \text{ ft}$

$2 \text{ ft}$

$1.5 \text{ in}$

$2.5\text{ in}$

$1.5 \text{ ft}$

Explanation

Ms. Johnson started with feet of yarn, however she only needs half of the feet.

To find the length of the amount of yarn that she needs, divide in half.

The solution is:

$\frac{5}{2}=2.5$

Mr. Lam is planning on painting a rectangular wall in his living room. Before he starts painting, he decided to take a few measurements of the wall. He finds out that the width of the wall is twice the measurement of the height of the wall. If the width of the wall is feet, what is the height of the wall?

$12\tfrac{1}{2} \text{ ft}$

$10\tfrac{1}{2} \text{ ft}$

$12\tfrac{3}{4} \text{ ft}$

$11\tfrac{3}{4} \text{ ft}$

Explanation

Since the height of the rectangular wall is half the length of the width, divide by

The solution is:

$25 \div2=12\tfrac{1}{2}$

Check:

$12\times2=24$
$2\times \frac{1}{2}=1$

Does the black line in the figure represent a line of symmetry?

Yes

Explanation

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line represents a line of symmetry because if you fold on the black line, then one side would lay on top of the other and the parts would match up.

How to find symmetry

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