Numbers & Operations with Fractions
5.NF.A.1
I can add and subtract fractions with unlike denominators (including mixed numbers) by using
equivalent fractions as a strategy to produce equivalent sums or differences of the fractions
with unlike denominators.
Vocabulary:
1. Numerator- top of the fraction, shows how much you have
2. Denominator- bottom of the fraction, shows how much there is in total
3. Unlike denominators- when the denominators of two or more fractions
are different
4. Like denominators- when the denominators of two or more fractions
are the same
Numbers & Operations with Fractions
5.NF.A.2
I can solve word problems involving addition and subtraction of fractions.
o
Decide whether to add or subtract and then solve.
Jack is making a family recipe. He uses 3/8 teaspoon of curry and 1/3
teaspoon of rosemary. How much spice does Jack use in all?
Stella had 7/8 of a bag of popcorn. She gave 5/6 of the bag to her friends.
How much does Stella have left?
Hailey builds a model car for a competition. The maximum car length allowed
is 8 3/4 inches. Hailey's car measures 6 9/16 inches. How much shorter is her
car than the maximum length allowed?
Jill and her brother Ray grow tomatoes. Jill picks 3 2/3 pounds and Ray picks
2 1/2 pounds. They give 4 pounds to Uncle Joe and the rest to Uncle Pete.
How many pounds of tomatoes do they give to Uncle Pete?
There were 5 1/4 gallons of water in an aquarium. Then Bruce added 2 2/3
gallons of water. If the aquarium holds 15 gallons, how many more gallons
does Bruce need to add to fill the aquarium?
Maria is writing a book report. The first week, she wrote 5/12 of the report
and the next week she wrote 1/4 of the report. What fraction of the whole
report has Maria completed?
Numbers & Operations with Fractions
5.NF.B.3
I can interpret a fraction as division of the numerator by the denominator. I can solve word
problems involving division of whole numbers leading to answers in the form of fractions or mixed
numbers.
o
Every fraction is a part of a whole. Anytime you divide up a whole into
parts, you make fractions. Fractions are division.
o
You can solve by drawing a picture:
Max is making 5 batches of chocolate chip cookies. He has 3 bags of
chocolate chips. How does he divide the chips equally into the batches?
Divide each bag into 5 equal pieces. Label each section batch 1-5 on each
bag.
Each batch of cookies gets ______ of the chocolate chips.
o
You can solve with division:
Nick brings 14 bags of granola on a hike to be shared equally among 5 people.
How much granola will each person get?
14 bags of granola divided among 5 people
14 divided among 5
14 ÷ 5 or 14/5
Now turn the division problem clockwise:
14
/5
Each person gets 14/5 of a bag of granola. You can also convert 14/5 to a
mixed number 14/5 = 2 4/5 bags of granola per person.
o
Answer each as a fraction:
3 ÷ 4=_________
o
7 ÷ 9=__________
5 ÷ 8=__________
Solve.
1. George and 5 friends must share 3 liters of juice. How much juice will
each person get?
2. Eric has 14 inches of wire. He wants to bend the wire to make a
triangle with 3 equal sides. How long will each side be?
3. Darren and his 2 sisters want to equally share 17 tokens at the arcade.
How many tokens will each of the get?
Numbers & Operations with Fractions
5.NF.B.4
I can apply and extend understandings of multiplication to multiply a fraction or whole number by
a fraction. I can apply this skill when solving area problems involving fractions.
o
When multiplying a fraction by a fraction, you do not need to make
common denominators. Multiply the numerators (tops) for an answer.
Multiply the denominators (bottoms) for an answer. The new fraction is your
answer. Check to see if it can be simplified.
X
o
=
When multiplying a fraction by a whole number, take the whole number
and put it over top of 1 (one) and turn it into a fraction. Then, multiply
fraction by fraction.
3X
o
=
X
=
If you see the word "of" in a problem, that is a clue that you multiply.
For example, if you need 1/4 of 6. 1/4 x 6 or 1/4 x 6/1
o
Solve and simplify.
X
=
X
=
X
5
X
4
=
=
A recipe calls for 6 cups of flour. Gunnar is only making 1/4 of the recipe.
How much flour does he need?
Sarah is 3/4 as old as Richardo. Richardo is 16 years old. How old is Sarah?
Jacob lives 3/10 mile from school. Mia lives 2/3 as far from school as Jacob.
How far does Mia live from school?
o Solve these area problems. Remember that area units are squared.
For example: 4cm2 or 4 squared cm
2
1
/3 yd
/2 m
3
4
/8 yd
/5 m
A private beach is 6/7 mile in length and 1/4 mile in width. What is the area
of the beach?
What is the area of a square with side lengths of 7/9 inches?
o
There is a short cut when multiplying fractions. Sometimes you can
cross cancel. This will eliminate reducing such large numbers at the end.
Look at the digits across from each other. Can they reduce?
X
The 9 and 11 cannot reduce because they do not have any numbers in common
that they can divide with.
The 5 and 15 can divide because they can both divide by 5. Divide both by 5
and write the new numbers in the problem.
1
X
o
Solve using cross cancelling
X
5
=
Numbers & Operations with Fractions
5.NF.B.5
I can interpret multiplication as scaling (resizing) by explaining why:
Multiplying a given number by a fraction greater than 1 results in a product greater than
the given number.
Multiplying a given number by a fraction less than 1 results in a product less than the given
number.
Vocabulary:
1. Scaling- resizing a number by using multiplication
o
Rule 1: When you multiply a number by a fraction less than 1, the
product is less than the number you started with.
Example: 3 X 1/4 = less than 3
o
because 3 X 1/4 = 3/4
Rule 2: When you multiply a number by a fraction greater than 1, the
product is greater than the number you started with.
Example: 3 X 5/4 = greater than 3
o
because 3 X 5/4 = 15/4 =33/4
Rule 3: When you multiply a number by a fraction equal than 1, the
product is equal to the number you started with.
Example: 3 X 4/4 = equal to 3
because 3 X 4/4 = 12/4 = 3
These rules will help you predict the size of your answer without doing the
actual math.
o
Apply It !
Do not work out the problem.
Instead, answer whether the answer will be greater than, less than, or equal
to.
8 X 6/6 = _______________ 8
Rule # _______
10 X 3/5 = _______________ 10
Rule # _______
16 X 7/4 = _______________ 16
Rule # _______
Answer with >, <, or =
1
/2 X 87 ____ 87
11
/12 X 8/11 ____ 8/11
5
/5 X 4/20 ____ 4/20
8
/7 X 10/13 ___ 10/13
A chef is making dinner for 12 people. She plans to use 1/4 pound of turkey
for each person. Will she need more than or less than 12 pounds of turkey?
Explain your reasoning.
Numbers & Operations with Fractions
5.NF.B.6
I can solve real world problems involving multiplication of fractions and mixed numbers.
o
It is possible to multiply fractions by fractions.
o
You CANNOT multiply fractions by mixed numbers.
o
You CANNOT multiply mixed numbers by mixed numbers.
Mixed numbers need to be converted into improper fractions before doing
any multiplication problem.
4 2/5 ft
3 1/2 ft
Convert each mixed number before multiplying.
4 2/5 = 22/5
3 1 / 2 = 7 /2
22
/ 5 X 7 /2 =
154
/10 = 15 2/5 ft2
o
Apply It !
Ross's grey mouse is 5 5/8 inches long. His white mouse is 1 1/2 times as long
as his grey mouse. How long is the white mouse?
A photograph is 3 1/2 inches by 4 1/2 inches. Find the area of the
photograph.
The original price of the comic book was $10, but it is on sale for 2/5 off the
original price. What is the sale price of the comic book?
Cheng made a batch of seafood gumbo. She made 5 1/2 servings of 1 2/3
cups. How many cups of gumbo did Cheng make?
Numbers & Operations with Fractions
5.NF.B.7
I can apply and extend understandings of division to divide unit fractions by whole numbers and
divide whole numbers by unit fractions. I can apply this skill when solving real-world problems
involving division with fractions.
o
You CANNOT divide fractions by fractions.
o
You CANNOT divide fractions by whole numbers.
o
You CANNOT divide whole numbers by fractions.
When there is a fraction division problem, change the problem to the
inverse, or opposite. Change the division sign to multiply. Flip the second
fraction over. If the second number is a whole number, put it over one and
flip it. Then multiply.
÷
÷
3
=
3
=
=
=
=
X
X
=
o
Apply It !
The May family plans to use 1/5 of their monthly budget for recreation. Mrs.
May further divides the recreation funds into 3 parts that are equal in
dollars. One part is going to be used for family day trips. What fraction of
the family's budget is going toward day trips?
Three people have 1/2 of a pizza to share equally. What fraction of the
whole pizza will each person get?
Sam has 1/7 meter of rope. He divides it into 2 equal parts. What fraction
of a meter is each part of rope?
Katie orders 5 pizzas. Each pizza is cut into eighths. How many pieces of
pizza does Katie have?
Hal works in a bakery. He used 1/6 of a large box of flour for a batch of
muffins. How many batches can he make with 4 boxes of flour?