Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Fractions with denominators of 10 and 100 are the bridge from fractions to decimals. Fourth graders learn that one tenth is the same amount as ten hundredths, so a fraction like 3/10 can be renamed 30/100. On a hundred grid, shading 3 full columns covers the same area as shading 30 small squares.
With that renaming in hand, students can add a fraction in tenths to a fraction in hundredths. To find 3/10 + 4/100, they rewrite 3/10 as 30/100 and add: 30/100 + 4/100 = 34/100. This is the only unlike-denominator addition fourth graders do, and it works because 100 is a multiple of 10. The standard prepares students for decimal notation, where 3/10 + 4/100 is written 0.3 + 0.04 = 0.34, and it reinforces the place value idea that ten of one unit make one of the next larger unit.
Money is a natural context: a dime is one tenth of a dollar and a penny is one hundredth.
Writing 3/10 + 4/100 = 7/110 shows students added everything. Renaming first so both fractions have denominator 100 avoids this.
Some students write 3/10 = 3/100. A hundred grid makes it clear that 3 columns are 30 squares, not 3.
Because 100 is bigger than 10, students assume hundredths are larger pieces. Cutting a tenth strip into ten tiny squares shows the opposite.
Find 6/10 + 25/100.
Answer: 6/10 + 25/100 = 85/100.
Hundred grids, base-ten blocks with the flat as one whole, and coins all show the ten-to-one relationship. Have students shade the same amount two ways, as columns and as single squares, and write both fractions.
Test items often pair this standard with decimals (4.NF.C.6), asking students to write the sum as a fraction and as a decimal. Linking the two notations early makes both standards easier.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 70/100
Multiply numerator and denominator by 10: (7 × 10)/(10 × 10) = 70/100.
Answer: 34/100
Rename 3/10 as 30/100. Then 30/100 + 4/100 = 34/100.
Answer: A) 35/100
2/10 = 20/100, and 20/100 + 15/100 = 35/100.
Answer: D) 4/10
Divide numerator and denominator by 10: 40/100 = 4/10.
Answer: 58/100
Each dime is 1/10 = 10/100 of a dollar, so 5 dimes are 50/100. Add 8 pennies (8/100): 58/100.
Answer: B) 11/100
1/10 = 10/100, so 10/100 + 1/100 = 11/100.
A full lesson with slides, activities and an exit ticket on tenths and hundredths as fractions, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.NF.C.5 with an answer key, ready in about a minute.
Make a worksheet →Turn tenths and hundredths as fractions into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Because 100 is ten times 10, tenths can always be renamed as hundredths, which lets students add them without general unlike-denominator methods. Those come in fifth grade.
It sets up 4.NF.C.6, where 34/100 is written as 0.34. The renaming of tenths as hundredths is the same idea as 0.3 = 0.30.