Notes for Solving Word Problems with Fractions. Step 1: Read the problem through completely. Look for key words. These key words will tell you whether to add, subtract, multiply or divide. Some word problems will require two or more operations. Step 2: Write the number sentence from the problem. Step 3: Solve the problem.
Example 1: Mickey has a piece of rope that is 10
2 feet long. If Mickey cuts the rope 3
into 16 equal pieces, how long will each piece be? Solution: Cut is the key word. If one cut were made, the operation would be subtraction. Since many cuts are being made, the operation is division. The number 2 2 . 3 3 2 The answer is feet. 3
sentence is: 10 รท 16 =
Example 2: Ellen paid 3
1 times as much for her first house as her parents paid for 2
their first house. If her parents paid $28,000 for their first house, how much did Ellen pay for her first house? 1 2
Solution: Times is the key words. The number sentence is 28, 000*3 = 98, 000 The answer is $98,000.
3 8
5 8
1 8
3 4
Example 3: Hazel worked the following hours this week: 5 , 6 ,8 ,8 . What is the total number of hours she has worked this week? How many more hours does she need to work to have 40 hours for the week?
3 8
5 8
1 8
Solution: The number sentence for the first question is 5 + 6 + 8 + 8
3 4
3 5 1 3 7 5 + 6 + 8 + 8 = 28 8 8 8 4 8
She has worked 28
7 hours so far this week. 8 7 8
1 8
The number sentence for the second question is 40 − 28 = 11 . 1 8
She needs to work 11 hours to complete 40 hours for the week.
Example 4: Jacob’s Market sold 12 Tuesday, and 13
1 1 feet of rope on Monday, 15 feet of rope on 3 6
1 feet on Wednesday. What is the total amount sold in the three 3
days?
Solution: The key word is total. We need to add the three amounts. 1 3
1 6
1 3
The answer is: 12 + 15 + 13 = 40
5 feet of rope 6
Example 5: Several lumber yards have reported their inventory of cord wood. What is the total cost of this inventory? Lumber yard
Amount of wood (cords)
Price
Lowes
3 4 3 117 4 1 105 3 1 198 2
$4
Amount of wood (cords)
Price
total
3 4 3 117 4 1 105 3 1 198 2
$4
$855
$4
$471
$3
$316
$4
$794
Alberts Dave’s Lumber Paty Lumber
Solution: Lumber yard Lowes Alberts Dave’s Lumber Paty Lumber The answer is: $2,436
213
213
total
$4 $3 $4
Example 6: Bill has a piece of wire that is 90
2 feet long. If Bill cuts the wire into 16 3
equal pieces, how long will each piece be? Solution: Cut is the key word. If one cut was made, the operation would be subtraction. Since many equal cuts are being made, the operation is division. The number sentence is: 90 The answer is 5
2 2 á 16 = 5 3 3
2 feet. 3
Example 7: Mary paid 4
1 times as much for her first house as her parents paid for 2
their first house. If her parents paid $20,000 for their first house, how much did Mary pay for her first house? 1 2
Solution: Times is the key words. The number sentence is $20, 000 Ă— 4 = $90,000 The answer is $90,000.
Example 8: Eddie Williams owns
2 1 of a company and Thomas Nash owns of the 5 3
company. If Jamie Davis owns the rest of the company, what part of the company does Jamie own? Solution: The total company is represented by 1 whole. 1-
2 1 - = 5 3
15 6 5 4 2 1 4 = or 1 - ( + ) = 15 15 15 15 5 3 15
3 8
Example 9: Tamara’s Cheese Market sold 24 pounds of cheese on Monday, 27 pounds of cheese on Tuesday, and 34
1 pounds of cheese on Wednesday. What is the 8
total amount of cheese sold in the three days? Solution: The key word is total. We need to add the three amounts. 3 8
The answer is: 24 + 27
1 4
1 1 3 + 34 = 85 pounds 4 8 4