Times a fraction can shrink: 5th grade math lesson

What this lesson shows

Fixes a mistake

63/65 × 20 is less than 20: multiplying by less than 1 shrinks.

The worked example

The lesson works this one step by step: 20 × 63/65. Then your kid tries one like it on paper.

The steps

Look at the fraction first
Top smaller than bottom: less than 1
Less than 1 shrinks

Helping at home

Multiplying does not always make bigger. Compare the fraction’s top and bottom: a top smaller than the bottom means less than 1, so the product is smaller than the number, even when the fraction is close to 1.

If your kid gets stuck

Write <, >, or =. Is the top smaller than the bottom?

Watch it with Lux

With Lux, this lesson is a narrated video and a printed page your kid works on. Then Lux helps with the same math on their own worksheet, one question at a time.

See how Lux works

Standards

Common Core 5.NF.B.5b
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

Matches standards in 42 statesSee each state's code

Alabama MA19.5.13b, MA19.5.13c
Alaska 5.NF.5.b
Arizona 5.NF.B.5.b
Arkansas 5.NPV.6
California 5.NF.B.5
Colorado 5.NF.B.5.b
Connecticut 5.NF.B.5
Delaware 5.NF.B.5
District of Columbia 5.NF.B.5
Florida MA.5.FR.2.3
Georgia 5.NR.3.5
Hawaii 5.NF.B.5
Idaho 5.NF.B.5.b
Illinois 5.NF.B.5
Iowa 5.NF.B.5.b
Kansas 5.NF.5.a, 5.NF.5.b
Kentucky KY.5.NF.5.b
Louisiana 5.NF.B.5.b, 5.NF.B.5.c, 5.NF.B.5.d
Maine 5.NF.B.5b
Maryland 4.NOS.E.13.a, 5.NOS.D.11.a, 5.NOS.D.12.a, 5.NOS.D.13.a, 5.NOS.D.14.b
Massachusetts 5.NF.B.5.b
Michigan 5.NF.B.5
Mississippi 5.NF.5a, 5.NF.5b
Missouri 5.NF.B.5.a, 5.NF.B.5.b, 5.NF.B.5.c, 5.NF.B.5.d
Montana MT.5.NF.5.a, MT.5.NF.5.b, 5.D1.14, 5.D4.5
Nevada 5.NF.B.5
New Hampshire 5.NF.B.5
New Jersey 5.NF.B.5b
New Mexico 5.NF.B.5
New York NY-5.NF.5.b
North Carolina NC.5.NF.4.b
North Dakota 5.NO.NF.2
Ohio 5.NF.5.b
Oregon 5.NF.B.5
Rhode Island 5.NF.B.5.a, 5.NF.B.5.b
South Dakota 5.NF.B.5.b
Tennessee 5.NF.B.5.a, 5.NF.B.5.b
Utah 5.NF.5.a, 5.NF.5.b
Vermont 5.NF.B.5
Washington 5.NF.B.5
West Virginia M.5.15
Wisconsin M.5.NF.B.5

Times a fraction can shrink