Question

1. jenna ran $2\frac{7}{8}$ kilometers each day for a week. how far did she run in all? give an estimate, then find the actual amount. show your work.

1. eduardo has a recipe that uses $\frac{2}{3}$ cup of flour for each batch. if he makes 4 batches, how many cups of flour will he need? how many cups of flour will he need in total if he makes 3 more batches? write your answers as mixed numbers. use the number line to help.

0 1 2 3 4

1. complete the equation. explain how you got your answer.

$\frac{6}{7} \times \frac{2}{5} = ?$

1. ted and his friends are rolling clay for art class. ted rolled out his clay until it was 2 feet long. noah rolled out his clay $\frac{3}{5}$ as long as teds clay. jeannine rolled out her clay until it was $1\frac{1}{2}$ times as long as teds clay. miles rolled out his clay $\frac{5}{5}$ as long as teds clay.

a. without completing the multiplication, whose clay is longer than teds clay? how can you tell?
b. without completing the multiplication, whose clay is shorter than teds clay? how can you tell?
c. whose clay is the same length as teds clay? how can you tell?

Explanation:

Problem 7

Step1: Estimate daily distance

Round $2\frac{7}{8}$ to 3 km.

Step2: Calculate estimated total

$3 \times 7 = 21$ km

Step3: Convert to improper fraction

$2\frac{7}{8} = \frac{23}{8}$ km

Step4: Calculate actual total

$\frac{23}{8} \times 7 = \frac{161}{8} = 20\frac{1}{8}$ km

Step1: Calculate for 4 batches

$\frac{2}{3} \times 4 = \frac{8}{3} = 2\frac{2}{3}$ cups

Step2: Find total batches

$4 + 3 = 7$ batches

Step3: Calculate for 7 batches

$\frac{2}{3} \times 7 = \frac{14}{3} = 4\frac{2}{3}$ cups

Step1: Multiply numerators/denominators

$\frac{6}{7} \times \frac{2}{5} = \frac{6 \times 2}{7 \times 5}$

Step2: Simplify the product

$\frac{12}{35}$

Answer:

Estimate: 21 kilometers
Actual amount: $20\frac{1}{8}$ kilometers

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Problem 8