Place Value with Decimal Fractions
Compare using >, <, or =
0.4 ____0.127
>
Find the products.
a. 1,900 × 20
b. 6,000 × 50
c. 250 × 300
a. 38,000
b. 300,000
c. 75,000
Show each expression on a number line. Solve.
a. 5/5 + 2/5
b. 6/3 + 2/3
a. 7/5; number line drawn
b. 8/3; number line drawn
Rewrite the division expression as a fraction and divide.
a. 3.2 ÷ 0.8 =
b. 3.2 ÷ 0.08 =
c. 7.2 ÷ 0.9 =
d. 0.72 ÷ 0.09 =
a. 3.2/0.8; 4
b. 3.2/0.08; 40
c. 7.2/0.9; 8
d. 0.72/0.09; 8
Farmer Jim keeps 12 hens in every coop. If Farmer Jim has 20 coops, how many hens does he have in all? If every hen lays 9 eggs on Monday, how many eggs will Farmer Jim collect on Monday? Explain your reasoning using words, numbers, or pictures.
Former Jim has 240 hens in all.
On Monday Farmer Jim will collect 2,160 eggs.
745 ÷ 1,000
0.745
Draw a model. Then, write the numerical expressions.
a. The difference between 8 forty-sevens and 7 forty-sevens
b. 6 times the sum of 12 a
a. (8 × 47) – (7 × 47)
b. 6 × (12 + 8)
Draw a model to help solve 5/6 + 1/4 . Write your answer as a mixed number
Accurate picture drawn; 1 1/12
Draw a picture that shows the division expression. Then, write an equation and solve.
a. 3 ÷ 9
b. 4 ÷ 3
a. 3 ÷ 9 = _3 9 = 1/3 or 27 ninths ÷ 9 = 3 ninths = 3/9 = 1/3 ; picture representing 3 ÷ 9 drawn
b. 4 ÷ 3 = 4/3 = 1 1/3 or 12 thirds ÷ 3 = 4 thirds = 4/3 = 1 1/3 ; picture representing 4 ÷ 3 drawn
The top surface of a desk has a length of 5.6 feet. The length is 4 times its width. What is the width of the desk?
1.4ft
3,632.1 ÷ 10 =
363.21
Draw an area model, and then solve using the standard algorithm.
a. 21 × 23 =
b. 143 × 12 =
a. 483
b. 1,716
Solve by drawing the rectangular fraction model.
1/2 + 1/5 =
Accurate picture drawn; 7/10
A baker made 9 cupcakes, each a different type. Four people want to share them equally. How many cupcakes will each person get?
Show how to solve the problem in Division Expression, Unit Form, Fractions and Mixed Numbers, and Standard Algorithm
9 ÷ 4; 36 fourths ÷ 4 = 9 fourths; 9/4 = 2 1/4 ; algorithm completed correctly; picture drawn representing 9 wholes, or 36 fourths, divided by 4
15 kilograms of rice are separated equally into 4 containers. How many kilograms of rice are in each container? Express your answer as a decimal and as a fraction.
Decimal form: 3.75
Fraction Form: 3 75/100
Write the following in exponential form and as a multiplication sentence using only 10 as a factor (e.g., 100 = 10² = 10 × 10)
1,000 =________ =__________
100 × 100 =_______ =__________
10^3 ; 10 × 10 × 10
10^4 ; 10 × 10 × 10 × 10
Solve.
a. Convert pounds to ounces. (1 pound = 16 ounces) 14 pounds =______ (× 1 pound)
=_____ × ( ounces)
=_______ ounces
b. Convert kilograms to grams.
18.2 kilograms =____ × (______ ) = × (_____ )
=_____ grams
a.14; 14, 16; 224
b. 18.2, 1 kilogram; 18.2, 1,000 grams; 18,200
For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. 1/2 – 1/7 =
b. 3/5 – 1/2 =
a. Accurate picture drawn; 5/14
b. Accurate picture drawn; 1/10
A grasshopper covered a distance of 5 yards in 9 equal hops. How many yards did the grasshopper travel on each hop?
a. Draw a picture to support your work.
b. How many yards did the grasshopper travel after hopping twice?
a. 5/9 yd; tape diagram drawn showing 5 ÷ 9
b. 1 1/9 yd
Matthew and his 3 siblings are weeding a flower bed with an area of 9 square yards. If they share the job equally, how many square yards of the flower bed will each child need to weed? Use a tape diagram to show your thinking
2 1/4; tape diagram drawn correctly
Convert using an equation with an exponent.
A. 2 meters to centimeters 2 m =______ cm
B. 40 millimeters to meters 40 mm =_______ m
A. 200; 2 × 102 = 200
B. 0.04; 40 ÷ 103 = 0.04
Solve.
Juwad picked 30 bags of apples on Monday and sold them at his fruit stand for $3.45 each. The following week he picked and sold 26 bags.
a. How much money did Juwad earn in the first week?
b. How much money did he earn in the second week?
c. How much did Juwad earn selling bags of apples these two weeks?
d. Extension: Each bag Juwad picked holds 15 apples. How many apples did he pick in two weeks? Write an expression to represent this problem.
a. $103.50
b. $89.70
c. $193.20
d. 15 × (30 + 26) = 840
Solve the word problem using the RDW strategy. Show all of your work. Mr. Pham mowed 2/7 of his lawn. His son mowed 1/4 of it. Who mowed the most? How much of the lawn still needs to be mowed?
Mr. Pham; 13/28
Olivia is half the age of her brother, Adam. Olivia’s sister, Ava, is twice as old as Adam. Adam is 4 years old. How old is each sibling? Use tape diagrams to show your thinking.
Olivia is 2 years old, and Ava is 8 years Old.
Hudson is choosing a seat in art class. He scans the room and sees a 4-person table with 1 bucket of art supplies, a 6-person table with 2 buckets of supplies, and a 5-person table with
Hudson should sit at a 5 person table with 2 buckets.