Proportionality>Converting Units Within a Measurement System Using Proportions and Unit Rates(TEKS.Math.6.4.H)
Help Questions
Texas 6th Grade Math › Proportionality>Converting Units Within a Measurement System Using Proportions and Unit Rates(TEKS.Math.6.4.H)
How many inches are in 3.5 feet? Use 12 inches = 1 foot.
42 inches
35 inches
36 inches
0.29 inches
Explanation
Unit rate: $3.5\text{ ft}\times \frac{12\text{ in}}{1\text{ ft}}=42\text{ in}$ (ft cancels). Proportion: $\frac{3.5\text{ ft}}{x\text{ in}}=\frac{1\text{ ft}}{12\text{ in}}\Rightarrow x=3.5\times 12=42$.
A recipe calls for 2 cups of milk, but your measuring tool is marked in fluid ounces only. How many fluid ounces should you pour? Use 1 cup = 8 fluid ounces.
8 fluid ounces
12 fluid ounces
20 fluid ounces
16 fluid ounces
Explanation
Unit rate: $2\text{ cups}\times \frac{8\text{ fl oz}}{1\text{ cup}}=16\text{ fl oz}$ (cups cancel). Proportion: $\frac{2\text{ cups}}{x\text{ fl oz}}=\frac{1\text{ cup}}{8\text{ fl oz}}\Rightarrow x=2\times 8=16$.
Which proportion can be used to convert 54 inches to y yards? Use 36 inches = 1 yard.
$\frac{54,\text{in}}{y,\text{yd}}=\frac{1,\text{yd}}{36,\text{in}}$
$\frac{54,\text{in}}{y,\text{yd}}=\frac{36,\text{in}}{1,\text{yd}}$
$\frac{y,\text{yd}}{54,\text{in}}=\frac{36,\text{in}}{1,\text{yd}}$
$\frac{36,\text{in}}{54,\text{in}}=\frac{y,\text{yd}}{1,\text{yd}}$
Explanation
Correct proportion: $\frac{54,\text{in}}{y,\text{yd}}=\frac{36,\text{in}}{1,\text{yd}}$. Cross-multiply: $54\cdot 1=36\cdot y\Rightarrow y=\frac{54}{36}=1.5,\text{yd}$. Unit rate: $54\text{ in}\times \frac{1\text{ yd}}{36\text{ in}}=1.5\text{ yd}$ (in cancels).
Convert 750 milliliters to liters. Use 1000 milliliters = 1 liter.
0.75 liters
1.33 liters
75 liters
0.075 liters
Explanation
Unit rate: $750\text{ mL}\times \frac{1\text{ L}}{1000\text{ mL}}=0.75\text{ L}$ (mL cancels). Proportion: $\frac{750\text{ mL}}{x\text{ L}}=\frac{1000\text{ mL}}{1\text{ L}}\Rightarrow 750\cdot 1=1000\cdot x\Rightarrow x=0.75$.