Adding Fractions and Mixed Numbers

What is 5/16 + 2 3/8?

• 3 15/16

• 2 7/16

• 2 11/16

• 3 3/16

Answer explanation

To solve this addition problem, begin by adding the fractional parts, 5/16 + 3/8. To add these fractions, find a common denominator, which is 16 (the least common multiple of 16 and 8). Now, convert 3/8 to an equivalent fraction with a denominator of 16 by multiplying both the numerator and denominator by 2: (3/8) × (2/2) = 6/16. Now, you have both fractions with a common denominator of 16:. 5/16 + 6/16 = 11/16. Now, combine the whole number part and fractional part: 2 (whole number part) + 11/16 (fractional part) = 2 + 11/16. So, the correct answer is 2 11/16.

Tags

CCSS.7.NS.A.1C

What is 2/3 + 5 3/4?

• 5 3/12

• 6 5/12

• 5 7/12

• 6 3/4

Answer explanation

To solve this addition problem, begin by adding the fractional parts, 2/3 + 3/4. To add these fractions, find a common denominator, which is 12. First, convert 2/3 to an equivalent fraction with a denominator of 12 by multiplying both the numerator and denominator by 4: (2/3) × (4/4) = 8/12. To express 3/4 with the same denominator as the other fraction, multiply both the numerator and denominator by 3: (3/4) × (3/3) = 9/12. Now, you have both fractions with a common denominator of 12, so add the fractions:: 8/12 + 9/12 = 17/12. Next, convert the improper fraction (17/12) to a mixed number (1 5/12) because 12 goes into 17 once with a remainder of 5. Now, combine the whole number parts and fraction part: 5 + 1 (whole number part) + 5/12 (fractional part) = 6 5/12/ So, the correct answer is 6 5/12.

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

What is 3 2/5 + 2 3/4?

• 6 3/20

• 5 1/20

• 5 9/20

• 6 9/20

Answer explanation

To solve this addition problem, begin by adding the fractional parts, 2/5 + 3/4. To add these fractions, find a common denominator, which is 20 (the least common multiple of 5 and 4). Now, convert 2/5 to an equivalent fraction with a denominator of 20 by multiplying both the numerator and denominator by 4: (2/5) × (4/4) = 8/20. Next, convert 3/4 to an equivalent fraction with a denominator of 20 by multiplying both the numerator and denominator by 5: (3/4) × (5/5) = 15/20. Now, you have both fractions with a common denominator of 20: 8/20 + 15/20 = 23/20. Then, convert the improper fraction (23/20) to a mixed number. Since 20 goes into 23 once with a remainder of 3, you can express 23/20 as 1 3/20. Now, combine the whole number parts and fractional parts: 3 (whole number part) + 2 (whole number part) + 1 (whole number part from the fractional part) + 3/20 (fractional part) = 3 + 2 + 1 + 3/20 = 6 + 3/20. So, the correct answer is 6 3/20.

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Emily is building a bookshelf. She already has a bookshelf that is 4 9/16 feet long, and she's building a new one that is 3 5/8 feet long. How long will the combined length of the bookshelves be once she finishes building the new one?

• 7 5/16

• 8 3/16

• 8 1/4

• 7 1/16

Answer explanation

To solve this addition problem, begin by adding the fractional parts, 9/16 and 5/8. To add these fractions, find a common denominator, which is 16 (the least common multiple of 16 and 8). Now, convert 5/8 to an equivalent fraction with a denominator of 16 by multiplying both the numerator and denominator by 2: (5/8) × (2/2) = 10/16. Now, you have both fractions with a common denominator of 16: 9/16 + 10/16 = 19/16. Next, convert the improper fraction (19/16) to the mixed number: Since 16 goes into 19 once with a remainder of 3, you can express 19/16 as 1 3/16. Now, combine the whole number parts and fractional parts: 4 (whole number part) + 3 (whole number part) + 1 (whole number part from the fractional part) + 3/16 (fractional part) = 8 + 3/16. So, the correct answer is 8 3/16 feet.

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2

Sam is planning a road trip. On the first day, he drives 2 1/2 hours to reach his first destination. On the second day, he drives 3 3/4 hours to get to his second stop. On the third day, he drives 4 2/3 hours to reach his final destination. How many hours did Sam spend driving during the entire road trip?

• 9 7/12 

• 10 3/4

• 11 1/4

• 10 11/12

Answer explanation

To find the total driving time, begin by adding the fractional parts of the driving hours: 1/2 + 3/4 + 2/3. To add these fractions, find a common denominator, which is 12 (the least common multiple of 2, 4, and 3). Now, convert each fraction to have a denominator of 12: 1/2 can be converted to 6/12 by multiplying both the numerator and denominator by 6; 3/4 can be converted to 9/12 by multiplying both the numerator and denominator by 3; 2/3 can be converted to 8/12 by multiplying both the numerator and denominator by 4. Now that all fractions have a common denominator of 12, add them: 6/12 + 9/12 + 8/12 = (6 + 9 + 8)/12 = 23/12. Next, convert the improper fraction to a mixed number because 23/12 is more than 1. So, divide 23 by 12: 23 ÷ 12 = 1 with a remainder of 11. So, the mixed number is: 1 (whole number part) + 11/12 (fractional part). Now, add the whole numbers: 2 (from Day 1) + 3 (from Day 2) + 4 (from Day 3) + 1 (whole number part from the fractional part) = 10. Combine the whole numbers and fractional parts: 10 (whole number part) + 11/12 (fractional part). So, Sam spent a total of 10 11/12 hours driving during the entire road trip.

Tags

CCSS.5.NF.A.1

CCSS.5.NF.A.2