Solving Word Problems with Fractional Lengths
Solving Word Problems with Fractional Lengths is a Grade 4 math skill in enVision Mathematics, Chapter 13: Measurement: Find Equivalence in Units of Measure. Students use fraction multiplication and unit conversions to solve real-world problems involving lengths expressed as fractions or mixed numbers.
Key Concepts
Property To solve word problems involving fractional lengths, convert all measurements to the same smaller unit. Use the conversion factor to multiply both the whole number and the fraction.
Examples A piece of wood is $3\frac{1}{2}$ feet long. How long is it in inches? $$3\frac{1}{2} \text{ feet} = (3 \times 12) + (\frac{1}{2} \times 12) = 36 + 6 = 42 \text{ inches}$$ Sarah has a ribbon that is $2\frac{1}{3}$ yards long. She cuts off a piece that is $4$ feet long. How many feet of ribbon does she have left? First, convert $2\frac{1}{3}$ yards to feet. $$2\frac{1}{3} \text{ yards} = (2 \times 3) + (\frac{1}{3} \times 3) = 6 + 1 = 7 \text{ feet}$$ Then, subtract: $7 4 = 3$ feet.
Explanation These problems require you to apply your knowledge of both fractions and customary unit conversions. First, identify the units used in the problem, such as feet, inches, or yards. Next, convert the measurements, including any fractions, into a common smaller unit by multiplying. Once all measurements are in the same unit, you can perform the necessary calculations like addition or subtraction to solve the problem.
Common Questions
How do you solve word problems with fractional lengths?
Identify the fractional lengths in the problem, convert units if needed, and apply multiplication or addition of fractions to find the required measurement.
Why do measurement problems involve fractions?
Real-world measurements are often not exact whole numbers. Rulers and measuring tools are divided into fractional parts like halves, quarters, and eighths of an inch.
What is an example of a fractional length word problem?
A ribbon is 3/4 of a foot long. How long is it in inches? Since 1 foot equals 12 inches, multiply 3/4 times 12 equals 9 inches.
How do you convert fractional measurements to different units?
Multiply the fractional length by the conversion factor. For example, to convert 1/2 yard to feet, multiply 1/2 times 3 (feet per yard) to get 3/2 or 1 and 1/2 feet.
What chapter covers fractional length problems in enVision Grade 4?
Solving word problems with fractional lengths is covered in Chapter 13: Measurement: Find Equivalence in Units of Measure in enVision Mathematics Grade 4.