**Math Problems and Solutions**

## Evaluate the Following (Addition of Fractions)

## 1. Evaluate the Following: 1/4 + 2/4

**Step 1:** Ensure the denominators are the same. Here, both fractions have a denominator of 4.

**Step 2:** Add the numerators: 1 + 2 = 3.

**Step 3:** Write the sum as a fraction: 3/4.

## 2. Evaluate the Following: 3/5 + 1/5

**Step 1:** Ensure the denominators are the same. Here, both fractions have a denominator of 5.

**Step 2:** Add the numerators: 3 + 1 = 4.

**Step 3:** Write the sum as a fraction: 4/5.

## 3. Evaluate the Following: 2/7 + 3/7

**Step 1:** Ensure the denominators are the same. Here, both fractions have a denominator of 7.

**Step 2:** Add the numerators: 2 + 3 = 5.

**Step 3:** Write the sum as a fraction: 5/7.

## 4. Evaluate the Following: 5/8 + 1/8

**Step 1:** Ensure the denominators are the same. Here, both fractions have a denominator of 8.

**Step 2:** Add the numerators: 5 + 1 = 6.

**Step 3:** Write the sum as a fraction: 6/8, which simplifies to 3/4.

## 5. Evaluate the Following: 4/9 + 2/9

**Step 1:** Ensure the denominators are the same. Here, both fractions have a denominator of 9.

**Step 2:** Add the numerators: 4 + 2 = 6.

**Step 3:** Write the sum as a fraction: 6/9, which simplifies to 2/3.

## 6. Evaluate the Following: 3/10 + 7/10

**Step 1:** Ensure the denominators are the same. Here, both fractions have a denominator of 10.

**Step 2:** Add the numerators: 3 + 7 = 10.

**Step 3:** Write the sum as a fraction: 10/10, which simplifies to 1.

## 7. Evaluate the Following: 6/11 + 2/11

**Step 1:** Ensure the denominators are the same. Here, both fractions have a denominator of 11.

**Step 2:** Add the numerators: 6 + 2 = 8.

**Step 3:** Write the sum as a fraction: 8/11.

## 8. Evaluate the Following: 2/5 + 4/10

**Step 1:** Find a common denominator. The least common multiple of 5 and 10 is 10.

**Step 2:** Convert 2/5 to 4/10.

**Step 3:** Add the fractions: 4/10 + 4/10 = 8/10, which simplifies to 4/5.

## 9. Evaluate the Following: 7/12 + 5/12

**Step 1:** Ensure the denominators are the same. Here, both fractions have a denominator of 12.

**Step 2:** Add the numerators: 7 + 5 = 12.

**Step 3:** Write the sum as a fraction: 12/12, which simplifies to 1.

## 10. Evaluate the Following: 1/3 + 2/5

**Step 1:** Find a common denominator. The least common multiple of 3 and 5 is 15.

**Step 2:** Convert 1/3 to 5/15 and 2/5 to 6/15.

**Step 3:** Add the fractions: 5/15 + 6/15 = 11/15.

## Evaluate the Following (Addition of Mixed Numbers)

## 11. Evaluate the Following: 2 1/4 + 3 2/4

**Step 1:** Add the whole numbers: 2 + 3 = 5.

**Step 2:** Add the fractions: 1/4 + 2/4 = 3/4.

**Step 3:** Combine the whole number with the fraction: 5 + 3/4 = 5 3/4.

## 12. Evaluate the Following: 4 3/5 + 2 2/5

**Step 1:** Add the whole numbers: 4 + 2 = 6.

**Step 2:** Add the fractions: 3/5 + 2/5 = 5/5 = 1.

**Step 3:** Combine the whole number with the fraction: 6 + 1 = 7.

## 13. Evaluate the Following: 5 2/7 + 1 4/7

**Step 1:** Add the whole numbers: 5 + 1 = 6.

**Step 2:** Add the fractions: 2/7 + 4/7 = 6/7.

**Step 3:** Combine the whole number with the fraction: 6 + 6/7 = 6 6/7.

## 14. Evaluate the Following: 3 1/2 + 2 1/2

**Step 1:** Add the whole numbers: 3 + 2 = 5.

**Step 2:** Add the fractions: 1/2 + 1/2 = 2/2 = 1.

**Step 3:** Combine the whole number with the fraction: 5 + 1 = 6.

## 15. Evaluate the Following: 6 1/8 + 2 3/8

**Step 1:** Add the whole numbers: 6 + 2 = 8.

**Step 2:** Add the fractions: 1/8 + 3/8 = 4/8 = 1/2.

**Step 3:** Combine the whole number with the fraction: 8 + 1/2 = 8 1/2.

## 16. Evaluate the Following: 7 2/9 + 3 4/9

**Step 1:** Add the whole numbers: 7 + 3 = 10.

**Step 2:** Add the fractions: 2/9 + 4/9 = 6/9 = 2/3.

**Step 3:** Combine the whole number with the fraction: 10 + 2/3 = 10 2/3.

## 17. Evaluate the Following: 4 5/6 + 1 1/6

**Step 1:** Add the whole numbers: 4 + 1 = 5.

**Step 2:** Add the fractions: 5/6 + 1/6 = 6/6 = 1.

**Step 3:** Combine the whole number with the fraction: 5 + 1 = 6.

## 18. Evaluate the Following: 8 3/4 + 2 2/4

**Step 1:** Add the whole numbers: 8 + 2 = 10.

**Step 2:** Add the fractions: 3/4 + 2/4 = 5/4 = 1 1/4.

**Step 3:** Combine the whole number with the fraction: 10 + 1 1/4 = 11 1/4.

## 19. Evaluate the Following: 3 7/10 + 4 2/10

**Step 1:** Add the whole numbers: 3 + 4 = 7.

**Step 2:** Add the fractions: 7/10 + 2/10 = 9/10.

**Step 3:** Combine the whole number with the fraction: 7 + 9/10 = 7 9/10.

## 20. Evaluate the Following: 2 2/3 + 1 4/3

**Step 1:** Add the whole numbers: 2 + 1 = 3.

**Step 2:** Add the fractions: 2/3 + 4/3 = 6/3 = 2.

**Step 3:** Combine the whole number with the fraction: 3 + 2 = 5.

## Evaluate the Following (Subtraction of Mixed Numbers)

## 21. Evaluate the Following: 5 3/4 - 2 1/4

**Step 1:** Subtract the whole numbers: 5 - 2 = 3.

**Step 2:** Subtract the fractions: 3/4 - 1/4 = 2/4 = 1/2.

**Step 3:** Combine the whole number with the fraction: 3 + 1/2 = 3 1/2.

## 22. Evaluate the Following: 6 2/5 - 3 1/5

**Step 1:** Subtract the whole numbers: 6 - 3 = 3.

**Step 2:** Subtract the fractions: 2/5 - 1/5 = 1/5.

**Step 3:** Combine the whole number with the fraction: 3 + 1/5 = 3 1/5.

## 23. Evaluate the Following: 7 1/2 - 2 3/2

**Step 1:** Subtract the whole numbers: 7 - 2 = 5.

**Step 2:** Subtract the fractions: 1/2 - 3/2 = -2/2 = -1.

**Step 3:** Combine the whole number with the fraction: 5 - 1 = 4.

## 24. Evaluate the Following: 8 1/6 - 3 4/6

**Step 1:** Subtract the whole numbers: 8 - 3 = 5.

**Step 2:** Subtract the fractions: 1/6 - 4/6 = -3/6 = -1/2.

**Step 3:** Combine the whole number with the fraction: 5 - 1/2 = 4 1/2.

## 25. Evaluate the Following: 4 3/4 - 1 5/4

**Step 1:** Subtract the whole numbers: 4 - 1 = 3.

**Step 2:** Subtract the fractions: 3/4 - 5/4 = -2/4 = -1/2.

**Step 3:** Combine the whole number with the fraction: 3 - 1/2 = 2 1/2.

## 26. Evaluate the Following: 5 2/9 - 1 7/9

**Step 1:** Subtract the whole numbers: 5 - 1 = 4.

**Step 2:** Subtract the fractions: 2/9 - 7/9 = -5/9.

**Step 3:** Combine the whole number with the fraction: 4 - 5/9 = 3 4/9.

## 27. Evaluate the Following: 7 5/8 - 2 3/8

**Step 1:** Subtract the whole numbers: 7 - 2 = 5.

**Step 2:** Subtract the fractions: 5/8 - 3/8 = 2/8 = 1/4.

**Step 3:** Combine the whole number with the fraction: 5 + 1/4 = 5 1/4.

## 28. Evaluate the Following: 6 3/10 - 2 1/10

**Step 1:** Subtract the whole numbers: 6 - 2 = 4.

**Step 2:** Subtract the fractions: 3/10 - 1/10 = 2/10 = 1/5.

**Step 3:** Combine the whole number with the fraction: 4 + 1/5 = 4 1/5.

## 29. Evaluate the Following: 8 2/3 - 3 4/3

**Step 1:** Subtract the whole numbers: 8 - 3 = 5.

**Step 2:** Subtract the fractions: 2/3 - 4/3 = -2/3.

**Step 3:** Combine the whole number with the fraction: 5 - 2/3 = 4 1/3.

## 30. Evaluate the Following: 7 4/5 - 2 1/5

**Step 1:** Subtract the whole numbers: 7 - 2 = 5.

**Step 2:** Subtract the fractions: 4/5 - 1/5 = 3/5.

**Step 3:** Combine the whole number with the fraction: 5 + 3/5 = 5 3/5.

## Evaluate the Following (Subtraction of Fractions)

## 31. Evaluate the Following: 7/8 - 2/8

**Step 1:** Subtract the fractions: 7/8 - 2/8 = 5/8.

## 32. Evaluate the Following: 5/6 - 1/6

**Step 1:** Subtract the fractions: 5/6 - 1/6 = 4/6 = 2/3.

## 33. Evaluate the Following: 3/4 - 1/4

**Step 1:** Subtract the fractions: 3/4 - 1/4 = 2/4 = 1/2.

## 34. Evaluate the Following: 9/10 - 3/10

**Step 1:** Subtract the fractions: 9/10 - 3/10 = 6/10 = 3/5.

## 35. Evaluate the Following: 7/12 - 2/12

**Step 1:** Subtract the fractions: 7/12 - 2/12 = 5/12.

## 36. Evaluate the Following: 4/5 - 1/5

**Step 1:** Subtract the fractions: 4/5 - 1/5 = 3/5.

## 37. Evaluate the Following: 5/9 - 2/9

**Step 1:** Subtract the fractions: 5/9 - 2/9 = 3/9 = 1/3.

## 38. Evaluate the Following: 8/15 - 4/15

**Step 1:** Subtract the fractions: 8/15 - 4/15 = 4/15.

## 39. Evaluate the Following: 11/20 - 5/20

**Step 1:** Subtract the fractions: 11/20 - 5/20 = 6/20 = 3/10.

## 40. Evaluate the Following: 7/8 - 5/12

**Step 1:** Find a common denominator: 24.

**Step 2:** Convert fractions: 7/8 = 21/24, 5/12 = 10/24.

**Step 3:** Subtract the fractions: 21/24 - 10/24 = 11/24.

## Word Problems (Addition and Subtraction with Mixed Numbers)

## 41. Jane had 3 1/2 liters of juice. She bought 2 3/4 more liters. How many liters does she have now?

**Step 1:** Add the whole numbers: 3 + 2 = 5.

**Step 2:** Add the fractions: 1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4.

**Step 3:** Combine the whole number with the fraction: 5 + 1 1/4 = 6 1/4 liters.

## 42. A recipe requires 4 1/2 cups of sugar. If you already added 2 2/3 cups, how much more sugar do you need to add?

**Step 1:** Subtract the whole numbers: 4 - 2 = 2.

**Step 2:** Subtract the fractions: 1/2 - 2/3 = 3/6 - 4/6 = -1/6.

**Step 3:** Combine the whole number with the fraction: 2 - 1/6 = 1 5/6 cups.

## 43. There were 7 1/2 meters of ribbon. After using 3 3/4 meters for a project, how much ribbon is left?

**Step 1:** Subtract the whole numbers: 7 - 3 = 4.

**Step 2:** Subtract the fractions: 1/2 - 3/4 = 2/4 - 3/4 = -1/4.

**Step 3:** Combine the whole number with the fraction : 4 - 1/4 = 3 3/4 meters.

## 44. Emily has 8 1/3 yards of fabric. She used 5 1/6 yards. How much fabric does she have left?

**Step 1:** Subtract the whole numbers: 8 - 5 = 3.

**Step 2:** Subtract the fractions: 1/3 - 1/6 = 2/6 - 1/6 = 1/6.

**Step 3:** Combine the whole number with the fraction: 3 + 1/6 = 3 1/6 yards.