Math Lesson 56 Adding and Subtracting with Like Denominators

Write each mixed number as an improper fraction. 1.) 6 1/3 2.) 2 1/5 3.) 3 2/7 4.) 8 1/2

1.) 6 1/3 = 19/3 2.) 2 1/5 = 11/5 3.) 3 2/7 = 23/7 4.) 8 1/2 = 17/2

like fractions

Fractions that have the same denominator.

Adding & Subtracting with Like Denominators

In this lesson, we learn to add and subtract fractions with like denominators. These are fractions that have the same denominator. One important thing to remember is when the numerator and denominator are the same, the fraction is equal to 1.

Common Error Alert

Many students mistakingly add or subtract both the numerator and denominator. Make sure you keep the denominator the same and only add or subtract the numerator.

Explain how to add or subtract like fractions.

So you add or subtract the top number, leaving the bottom number the same and then simplify if you need to. Example 1/4 + 2/4 = 3/4

Describe in words how to add 3 2/5 and 1 1/5 and how to subtract them.

To add the numbers, first add the fraction parts together: 2/5 + 1/5 = 3/5. Next add the whole numbers together: 3 + 1 = 4. Write them together: 4 3/5 To subtract the numbers, first subtract the fraction parts: 2/5 - 1/5 = 1/5. Next subtract the whole numbers: 3 - 1 = 2. Write them together: 2 1/5

Subtract, then write the answer in simplest form. 4 6/11 - 3 5/11 a. 1 1/11 b. 2 3/11 c. 8 d. 6/11

a. 1 1/11

Evaluate the expression for n = 1 19/20. Write the answer in simplest form. n = 1/20 a. 1 9/10 b. 1 c. 2 d. 19/20

a. 1 9/10

Peter surveyed his friends and family to see what they like to drink with breakfast. he found that 1/8 of the people like to drink grapefruit juice and 3/8 of them like to drink orange juice. the rest prefer either milk or coffee. What part of the people surveyed prefer grapefruit or orange juice with breakfast? Write your answer in simplest form. a. 1/2 b. 1/4 c. 1/16 d. 3/16

a. 1/2

Subtract, and write the answer in simplest form. 5 3/8 - 3 1/8 a. 2 1/2 b. 2 13/16 c. 8 3/4 d. 1 1/4

a. 2 1/2

Add, and write the answer in simplest form. 26/75 + 24/75 a. 2/3 b. 48/75 c. 24/25 d. 16/25

a. 2/3

Subtract, and write the answer in simplest form. 5 3/8 - 3/8 a. 5 1/4 b. 2 13/16 c. 6 d. 2 5/8

a. 5 1/4

Sean orders a pizza for himself and his friend Christopher. Christopher is late arriving at Sean's house so Sean begins eating without him. a. If Sean easts 5/12 of the pizza, how much is left? Show your work. b. When Christopher arrives, he eats 5/12 of the pizza also. How much did the boys eat together? How much is left over? Write the fractions in simplest form, and show your work.

a. 7/12 because 1 = 12/12 and 12/12 - 5/12 = 7/12. b. They eat 5/12 + 5/12 which = 10/12 or 5/6. The amount left over is 12/12 - 10/12 = 2/12 or 1/6.

Evaluate the expression for q = 1 5/11. Write the answer in simplest form. q - 1/11 a. 1 6/11 b. 1 4/11 c. 17/22 d. 15/22

b. 1 4/11

Regina and her mom are helping clean the cafeteria tables. Regina cleaned 3/10 of them, and her mom cleaned 1/10 of them. How many did they clean altogether? Write your answer in simplest form. a. 1/5 b. 2/5 c. 1/10 d. 5/2

b. 2/5

Add, and write the answer in simplest form. 1/16 + 9/16 a. 10/16 b. 5/8 c. 1/2 d. 3/4

b. 5/8

Evaluate the expression for w = 11/14. Write the answer in simplest form. w + 1/14 a. 5/7 b. 6/7 c. 3/7 d. 5/14

b. 6/7

Subtract, and write the answer in simplest form. 1 5/9 - 2/9 a. 1 7/9 b. 2/3 c. 1 1/3 d. 7/9

c. 1 1/3

A concert was 2 1/4 hour long. The first musical piece lasted 1/4 hour. The intermission also lasted 1/4 hour. How long was the rest of the concert? a. 2 hour b. 1 1/2 hour c. 1 3/4 d. 1 1/4

c. 1 3/4

Wesley drinks 2/13 gallon of juice each day. Find the number of gallons Wesley drinks in 5 days. Write your answer in simplest form. a. 7/13 gallon b. 2/18 gallon c. 10/13 gallon d. 7/18 gallon

c. 10/13 gallon

Estimate the sum or difference. 14 3/5 - 8/9 a. 15 b. 16 c. 14 d. 13

c. 14

Which number is closest to 5? a. 4 3/4 b. 4 2/6 c. 4 7/8 d. 4 1/3

c. 4 7/8

Evaluate the expression for w = 11/16. Write the answer in simplest form. w + 9/16 a. 5/8 b. 1/8 c. 1/16 d. 1 1/4

d. 1 1/4

Round each number to the nearest half. 1 3/4 a. 3 b. 1.75 c. 7/4 d. 2

d. 2

Subtract, and write the answer in simplest form. 2 5/7 - 2 3/7 a. 5 1/7 b. 1/7 c. 1 5/14 d. 2/7

d. 2/7

Evaluate each expression for x = 3/8. Write each answer in simplest form. x + 1 1/8 = 3/8 + 1 1/8=

x + 1 1/8 = 3/8 + 1 1/8= x = 1 4/8

Adding with Like Denominators. Steven plants a young oak tree in his backyard. The distance around the trunk grows at a rate of 1/8 inch per month. Find how much this distance will increase in two months. Write your answer in simplest form.

•Add just the Numerators (top numbers) •Leave the Denominators (bottom numbers) the same •Simplify 1 + 1 = 2 = 1 -- -- -- -- 8 8 8 4

Subtracting Like Denominator Fractions

•Only subtract the Numerators!!! •If a numerator and the denominator are the same, it equals 1. Subtract. Write your answer in simplest form. 1 - 2/3 = 3/3 - 2/3 = 1/3

Subtracting Mixed Numbers

•Subtract the Fractions •Then subtract the Whole Numbers Subtract. 3 7/12 - 1 1/12 = 2 6/12 = 2 1/2