Add Fractions and Mixed Numbers with Denominators of 10 and 100
This Grade 4 Eureka Math skill teaches students to add fractions and mixed numbers with denominators of 10 and 100 by converting tenths to hundredths to create a common denominator. Students learn that 3/10 becomes 30/100 before adding, and that mixed number addition requires adding whole parts and fractional parts separately. When the fractional sum is improper, students convert it — for example, 4/8/10 + 2/35/100 yields 6 + 115/100, which regroups to 7 and 15/100. This foundational decimal fraction skill appears in Chapter 32 of Eureka Math Grade 4.
Key Concepts
To add fractions or mixed numbers with denominators of 10 and 100, first find a common denominator by converting tenths to hundredths. For mixed numbers, add the whole number parts and the fractional parts separately. $$A\frac{b}{10} + C\frac{d}{100} = (A+C) + (\frac{b \times 10}{100} + \frac{d}{100})$$.
Common Questions
How do you add a fraction with denominator 10 to one with denominator 100?
Multiply the numerator and denominator of the tenths fraction by 10 to convert it to hundredths. For example, 3/10 becomes 30/100. Then add the numerators: 30/100 + 51/100 = 81/100.
What do you do when the sum of fractions is improper after adding?
Convert the improper fraction to a mixed number. For example, 115/100 = 1 and 15/100. Then add that whole number to the sum of the whole number parts.
How do you add mixed numbers with denominators 10 and 100?
Add whole number parts together, convert the tenths fraction to hundredths, then add the fractional parts. If the fractional sum is improper, regroup and add to the whole number sum.
Why must tenths be converted to hundredths before adding?
Fractions can only be added when they share the same denominator (like units). Since 10 and 100 are different, you must find a common denominator of 100 by multiplying the tenths fraction by 10/10.
What is an example of adding 4/8/10 and 2/35/100?
Convert 8/10 to 80/100. Add whole parts: 4+2=6. Add fractions: 80/100+35/100=115/100=1 and 15/100. Final answer: 7 and 15/100.