Join Tenths and Hundredths with a Common Unit
Multiply a tenths numerator and denominator by ten.
About 20 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For 4/10+9/100, rename 4/10 as 40/100.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A tenth contains ten hundredths. Rename a tenths fraction as hundredths before combining it with hundredths. The common denominator means all pieces have the same size. Then convert the resulting fraction to decimal notation. Adding denominators would change the unit size incorrectly.
Multiply a tenths numerator and denominator by ten. Add the hundredths numerators, keep denominator one hundred, and write the decimal. Use a grid to check the total shaded small squares.
Convert tenths to hundredths before adding their counts. Keep the common denominator; do not add the denominators. Mark full ten-square rows for tenths and individual squares for hundredths.
- Mark full ten-square rows for tenths and individual squares for hundredths.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Multiply a tenths numerator and denominator by ten.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
For 4/10+9/100, rename 4/10 as 40/100. Join forty and nine hundredths to get 49/100=0.49. The denominator stays one hundred because the joined pieces are still hundredths. Writing 13/110 would not represent the supplied equal-size pieces. Convert tenths to hundredths before adding their counts. Keep the common denominator; do not add the denominators. Mark full ten-square rows for tenths and individual squares for hundredths.
Check your reasoning
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Helpful tips
- Convert tenths to hundredths before adding their counts.
- Keep the common denominator; do not add the denominators.
See the answer and explanation
0.27
Rename each tenth as ten hundredths before joining. The result is 0.27.
Take it further
Find 6/10+14/100. Expected: 74/100=0.74.
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