Subtracting Mixed Numbers-Unlike Denominators-Gr 5-Solved Examples

Solved Examples and Worksheet for Subtracting Mixed Numbers-Unlike Denominators

Q1Paula baked 513 lb of cookies for a sale and 356 lb of the cookies were sold. How many pounds of the cookies were left?

A. 112 lb
B. 312 lb
C. 212 lb
D. None of the above

Solutions

Step: 1

The cookies left over = 513 - 356

Step: 2

= 526 - 356

[Write an equivalent fraction for 13 with LCD 6 as denominator.]

Step: 3

= 486 - 356

[Since 56 > 26, rewrite 526 as 4 + 126 = 486.]

Step: 4

= (4 - 3) + (86 - 56)

[Subtract the whole numbers and fractions.]

Step: 5

= 136

Step: 6

112 lb of cookies were left.

Correct Answer is : 112 lb

Q2Jake bought 613 lb of corn chips. He gave 215 lb of it to his brothers. Find the weight of chips left in the bag.

A. 4215 lb
B. 6215 lb
C. 3215 lb
D. 5215 lb

Solutions

Step: 1

The corn chips left = 613 - 215

Step: 2

= (6 - 2) + (13 - 15)

[Separate the whole numbers and fractions.]

Step: 3

= (6 - 2) + (515 - 315)

[Rewrite the fractions with same denominator.]

Step: 4

= 4 + 215

[Subtract the whole numbers and fractions.]

Step: 5

= 4215

[Simplify the fraction and combine the two terms.]

Step: 6

4215 lb of corn chips is left in the bag.

Correct Answer is : 4215 lb

Q3Tanya bought 956 gallons of milk. She used 523 gallons of it to make ice cream. How much milk is left?

A. 416
B. 413
C. 427
D. 414

Solutions

Step: 1

The milk left = 956 - 523

Step: 2

= (9 - 5) + (56 - 23)

[Separate whole numbers and the fractions.]

Step: 3

= (9 - 5) + (56 - 46)

[Use LCD 6 to rewrite the fractions with same denominator and subtract.]

Step: 4

= 4 + 16

[Subtract the whole numbers and the fractions.]

Step: 5

= 416

[Simplify the fraction and combine the two terms.]

Step: 6

The milk left is 416 gallons.

Correct Answer is : 416

Q4Tim bought a rope of length 534 in., of which he used 223 in. Find the length of the remaining rope.

A. 223 in.
B. 1213 in.
C. 3112 in.
D. 914 in.

Solutions

Step: 1

534 - 223

[Write expression for the difference between the lengths.]

Step: 2

= (5 - 2) + (34 - 23)

[Write the whole numbers and the fractions separately.]

Step: 3

= (5 - 2) + (912 - 812)

[Rewrite the fractions with same denominator using the L.C.D, 12.]

Step: 4

= 3 + 112

[Add.]

Step: 5

= 3112

[Write the sum as mixed number.]

Step: 6

The length of the rope remaining is 3112 in.

Correct Answer is : 3112 in.

Q5Find the difference between 42130 and 3025 .
A. 111930
B. 1123
C. 111115
D. None of the above

Solutions

Step: 1

42130 - 3025

[Original expression.]

Step: 2

= 42130 - 301230

[Use LCD 30 to write the equivalent fraction of 25.]

Step: 3

= 413130 - 301230

[Since 130 < 1230, rewrite 42130 as 41 + 1130 = 413130.]

Step: 4

= (41 - 30) + (3130 - 1230)

[Write the whole numbers and fractions separately.]

Step: 5

= 11 + 1930

[Subtract the whole numbers and fractions.]

Step: 6

= 111930

[Combine the two terms.]

Step: 7

The difference of 42130 and 3025 is 111930.

Correct Answer is : 111930

Q6Jim wants to prepare 313 cups of a mixture of milk and water. He takes 214 cups of milk and uses water for the remaining part. How much water is added in the mixture?
A. 1112 cups
B. 114 cups
C. 214 cups
D. 118 cups

Solutions

Step: 1

Total quantity of mixture = 313 cups

Step: 2

Amount of milk in the mixture = 214cups

Step: 3

Amount of water in the mixture = Amount of total mixture - Amount of milk in the mixture

Step: 4

= 313 cups - 214 cups

Step: 5

= 3412 - 2312

[Multiply the numerator and denominator of 13 with 4 and 14 with 3 to make the denominators equal.]

Step: 6

= 1112

[Subtract whole numbers and subtract fractions.]

Step: 7

So, 1112 cups of water is added in the mixture.

Correct Answer is : 1112 cups

Q7Sheela baked 713 lb of cookies for a sale, and 456 lb of cookies were sold. Find the amount of cookies that is left.

A. 412 lb
B. 312 lb
C. 212 lb
D. 512 lb

Solutions

Step: 1

The cookies left over = 713 - 456

Step: 2

= 726 - 456

[Write an equivalent fraction for 13 with LCD 6 as denominator.]

Step: 3

= 686 - 456

[Since 56 > 26, rewrite 726 as 6 + 126 = 686.]

Step: 4

= (6 - 4) + (86 - 56)

[Subtract the whole numbers and fractions.]

Step: 5

= 236

Step: 6

212 lb cookies were left.

Correct Answer is : 212 lb

Q8Jerald bought 615 lb of cookies bag. On his way back he ate 417 lb of it. Find the weight of cookies left in the bag.

A. 10235lb
B. 22lb
C. 2235lb
D. 101235lb

Solutions

Step: 1

The cookies left = 615 - 417

Step: 2

(6 - 4) + (15 - 17)

[Separate the whole numbers and fractions.]

Step: 3

= (6 - 4) + (735 - 535)

[Rewrite the fractions with same denominator.]

Step: 4

= 2 + 235

[Subtract the whole numbers and fractions.]

Step: 5

= 2235

[Simplify the fraction and combine the two terms.]

Step: 6

2235 lb of cookies is left in the bag.

Correct Answer is : 2235lb

Q9Subtract:
1434 - 612

A. 738
B. 814
C. 714
D. 918

Solutions

Step: 1

1434 - 612

[Original expression.]

Step: 2

= 1434 - 624

[Rewrite the fractional part in the mixed number 612 with a denominator of 4.]

Step: 3

= 814

[Subtract the whole numbers. Subtract the fractions.]

Correct Answer is : 814

Q10Which of the following is the difference between the mixed numbers 314 and 712?

A. 313
B. 434
C. 414
D. 423

Solutions

Step: 1

712 - 314

[Original expression.]

Step: 2

= 724 - 314

[Rewrite the fractional part in the mixed number 712 with a denominator of 4.]

Step: 3

= 414

[Subtract the whole numbers. Subtract the fractions.]

Correct Answer is : 414

Q11Subtract:
434 - 123 =

A. 5112
B. 51112
C. 31112
D. 3112

Solutions

Step: 1

434 - 123

Step: 2

= 43 × 34 × 3 - 12 × 43 × 4

[Rewrite the fractional part of the mixed numbers so that they have the same denominator.]

Step: 3

= 4912 - 1812

Step: 4

= 3112

[Subtract the whole numbers and the fractions.]

Step: 5

So, 434 - 123 = 3112

Correct Answer is : 3112

Q12Subtract:
623 - 212 =
A. 456
B. 516
C. 356
D. 416

Solutions

Step: 1

623 - 212

Step: 2

= 62 × 23 × 2 - 21 × 32 × 3

[Rewrite the fractional part of the mixed numbers so that they have the same denominator.]

Step: 3

= 646 - 236

Step: 4

= 416

[Subtract the whole numbers and the fractions.]

Step: 5

So, 623 - 212 = 416

Correct Answer is : 416

Solved Examples and Worksheet for Subtracting Mixed Numbers-Unlike Denominators

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HighSchool Math