Eureka Math Lesson 11 Homework 5.3 Answer Key

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Section 1

a. Generate equivalent fractions to get the same unit, then subtract.
b. ½ – 1/3 =
c. 7/10 – 1/3 =
d. 7/8 – ¾ =
e. 1 2/5 – 3/8 =
f. 1 3/10 – 1/6 =
g. 2 1/3 – 1 1/5 =
h. 5 6/7 – 2 2/3 =

Draw a number line to show your answer to (g) is reasonable

Answer:

a. ½ – 1/3 = 1/2 – 1/3 = 3/6 – 2/6 = 1/6
b. 7/10 – 7/3 = 7/10 – 1/3 = 21/30 – 10/30 = 11/30
c. 7/8 – ¾ = 7/8 – (3/4 x 2) = 7/8 – 6/8 = 1/8
d. 1 2/5 – 3/8 = 7/5 – 3/8 = 56/40 – 15/40 = 41/ 40 = 1 1/40
e. 1 3/10 – 1/6 = 13/10 – 1/6 = 39/30 – 5/30 = 34/30 = 1 4/30
f. 2 1/3 – 1 1/5 = 7/3 – 6/5 = 7/3 – 6/5 = 35/15 – 18/15 = 17/15 = 1 2/15
g. 5 6/7 – 2 2/3 = 5 6/7 – 2 – 2/3 = 3 + 6/7 – 2/3
= 3 + 6/7 – 2/3 = 3 + 18/21 – 14/21 = 3 4/21
h.

George says that too subtract fractions with different denominators, you always have to multiply the denominators to find the common unit, for example:

3/8 – 1/6 = 18/48 – 8/48 = 10/ 48

Show George how he could have chosen a denominator smaller than 48, and solve the problem.

Answer:

8: 8 16 24

6: 6 12 18 24

The (LCM) lowest Common Multiple is actually 24 not 48.

(3/8 x 3) – (1/6 x 4) = 9/24 – 4/24 = 5/24 = 10/48

Meiling has 1 ¼ liter of orange juice. She drinks 1/3 liter. How much orange juice does she have left? (Bonus: If her brother then drinks twice as much as Meiling, how much is left?

Answer:

1 ¼ – 1/3 = 5/4 – 1/3 = 15/12 – 4/12 = 11/12 (Liters of juice left)

Bonus: twice of Meiling = 2/3 à 11/12 – (2/3 x 4) = 11/12 – 8/12 = 3/12

Harlan used 3 ½ kg of sand to make a large hourglass. To make a small hourglass he only used 1 3/7 kg of sand. How much more sand does it take to make the large hourglass than the small one?

Answer:

3 ½ – 1 3/7 = 3 7/14 – 1 6/14 = 2 1/14. So, 2 1/14 kg of sand more in the larger hourglass.

Section 2

First find a common unit, then subtract.

a. ½ – 1.5 =
b. 7/8 – 1/3 =
c. 7/10 – 3/5 =
d. 1 5/6 – 2/3 =
e. 2 ¼ – 1 1/5 =
f. 5 6/7 – 3 2/3 =
g. 15 7/8 – 5 ¾ =
h. 15 5/8 – 3 1/3 =

Answer:

a. ½ – 1/5 = ½ – 1/5 = 5/10 – 2/10 = 3/10
b. 7/8 – 1/3 = 7/8 – 1/3 = 21/24 – 8/24 = 13/24
c. 7/10 – 3/5 = 7/10 – (3/5 x 2) = 7/10 – 6/10 = 1/20
d. 1 5/6 – 2/3 = 11/6 – (2/3 x 2) = 11/6 – 4/6 = 7/6 = 1 1/6
e. 2 ¼ – 1 1/5 = 2 ¼ – 1 – 1/5 = 1 ¼ – 1/5 = 5/4 – 1/5 = 25/20 – 4/20 = 2/10 = 1 1/20
f. 5 6/7 – 3 2/3 = 5 6/7 – 3 – 2/3 = 2 6/7 – 2/3 = 20/7 – 2/3 = 60/21 – 14/21
= 46/21 = 2 4/21
g. 15 7/8 – 5 ¾ = 15 7/8 – 5 – ¾ = 10 7/8 – 2/4 = 10 7/8 -6/8 = 10 1/8
h. 15 5/8 – 3 1/3 = 15 5/8 – 3 1/3 = 15 15/24 – 3 8/24 = 12 7/24

Sandy ate 1/6 of a candy bar. John ate ¾ of it. How much more of the candy did John eat than Sandy?

Answer:

¾ – 1/6 = 9/12 – 2/12 = 7/12. So, John ate 7/12 more than Sandy.

4 ½ yards of cloth are needed to make a woman’s dress. 2 2//7 yards of cloth are needed to make a girl’s dress. How much more cloth is needed to make a woman’s dress than a girl’s dress?

Answer:

4 ½ – 2 2/7 = 4 7/14 – 2 4/14 = 2 3/14. So, a woman’s dress needs 2 3/14 yards more cloth.

Bill reads 1/5 of a book on Monday. He reads 2/3 of the book on Tuesday. If he finishes reading the book on Wednesday, what fraction of the book did he read on Wednesday?

Answer:

1 – 1/5 – 2/3 = (5/5 – 1/5) – 2/3 = 4/5 – 2/3 = 12/15 – 10/15 = 2/15.

So, 2/15 of the book was read by Bill on Wednesday