Lesson 7 Fractions as Sums

- Let’s write fractions as sums.

Warm-up Choral Count: Three-fourths at a Time

Count by $\frac{3}{4}$ , starting at $\frac{3}{4}$ .

Activity 1 Barley Soup

2 stacked measuring cups labeled one fourth cup and three fourths cup.

Lin is learning to make barley soup using a family recipe. Here are some ingredients in the recipe:

$\frac{3}{4}$ cup of barley
$\frac{5}{4}$ cups of chopped celery
$\frac{6}{4}$ cups of chopped carrots

1 cup of chopped onions
$2 \frac{1}{4}$ cups of vegetable broth

Lin has only one measuring cup that measures $\frac{1}{4}$ cup. Show how Lin could use the cup to measure the right amount of each ingredient.
- Barley:
- Celery:
- Carrots:
- Onions:
- Vegetable broth:
Lin later found a $\frac{3}{4}$ -cup measuring cup. Show how she could use the cups to measure the right amount of each ingredient.
- Barley:
- Celery:
- Carrots:
- Onions:
- Vegetable broth:

Activity 2 Sums in Fifths and Thirds

Use different combinations of fifths to make a sum of $\frac{9}{5}$ .
1. $\frac{9}{5} =$ $+$ $+$ $+$ $+$
2. $\frac{9}{5} =$ $+$ $+$ $+$
3. $\frac{9}{5} =$ $+$ $+$
4. $\frac{9}{5} =$ $+$
Write different ways to use thirds to make a sum of $\frac{4}{3}$ . How many can you think of? Write an equation for each combination.
Is it possible to write any fraction with a denominator of 5 as a sum of other fifths? Explain or show your reasoning.

Practice Problem

Problem 1

Write $\frac{4}{3}$ in as many ways as you can as a sum of fractions.
Write $\frac{9}{8}$ in at least 3 different ways as a sum of fractions.