CaliforniaBasic Skills

Free CBEST Mathematics Study Guide

Comprehensive study materials covering all CBEST competencies. Complete preparation for the CBEST Mathematics section. Covers estimation, computation, and numerical reasoning through targeted study guides and practice tests.

21 Study Lessons
3 Content Areas
50 Exam Questions
41 Passing Score

What You'll Learn

Estimation, Measurement, and Statistical Principles30%
Computation and Problem Solving35%
Numerical and Graphic Relationships35%

Free Study Guide - Lesson 1

30 min read
U.S. Units of Measurement

Learn the standard U.S. units for length, temperature, weight, and capacity — what they are, when to use them, and how to convert between common units in real-world school and workplace settings.

Learning Outcomes

  • Recall the standard U.S. customary units for length (inches, feet, yards, miles), weight (ounces, pounds, tons), and liquid volume (fluid ounces, cups, pints, quarts, gallons)
  • Convert between units within each measurement category using multiplication and division
  • Solve multi-step conversion problems that appear in CBEST word problems
  • Select the most appropriate unit of measurement for a given real-world situation

(1) Length Conversions

The U.S. customary system for length uses four main units: inches, feet, yards, and miles. The foundational rule for all unit conversions: when moving from a larger unit to a smaller unit, multiply; when moving from a smaller unit to a larger unit, divide. This rule prevents the most common conversion errors on the CBEST.

Equivalency Example Problem Solution
12 inches = 1 foot How many inches in 4.5 feet? 4.5 × 12 = 54 inches
3 feet = 1 yard How many yards in 15 feet? 15 ÷ 3 = 5 yards
36 inches = 1 yard How many inches in 2.5 yards? 2.5 × 36 = 90 inches
5,280 feet = 1 mile How many feet in 2.5 miles? 2.5 × 5,280 = 13,200 feet
Worked Example — Multi-Step Length Conversion

A hallway is 180 inches long. Express this measurement in yards.

Step 1: Convert inches to feet: 180 ÷ 12 = 15 feet
Step 2: Convert feet to yards: 15 ÷ 3 = 5 yards
TEST READY TIP

On the CBEST, length conversion problems often use multi-step chains. Work one unit at a time. Going from inches to yards, you must pass through feet — never skip directly unless you know the combined conversion factor (36 inches = 1 yard). Writing each step prevents errors.

(2) Weight Conversions

U.S. customary weight uses three units on the CBEST: ounces, pounds, and tons. Remember: 16 ounces = 1 pound and 2,000 pounds = 1 ton. These two equivalencies are everything you need for weight problems on the exam.

Equivalency Convert TO smaller (multiply) Convert TO larger (divide)
16 ounces = 1 pound 3 lb × 16 = 48 oz 48 oz ÷ 16 = 3 lb
2,000 pounds = 1 ton 4 tons × 2,000 = 8,000 lb 8,000 lb ÷ 2,000 = 4 tons
Worked Example — Weight Problem

A school supply shipment weighs 3.5 tons. How many pounds is that?

Answer: 3.5 × 2,000 = 7,000 pounds

(3) Volume and Capacity Conversions

Liquid volume in the customary system uses a chain of five units. Memorize them in order from smallest to largest: fluid ounces → cups → pints → quarts → gallons. Each step in the chain has its own conversion factor.

Equivalency Memory Aid
8 fluid ounces = 1 cup A standard cup of coffee = 8 fl oz
2 cups = 1 pint A pint of cream cheese holds 2 cups
2 pints = 1 quart Quarter (of a gallon) = 1 quart
4 quarts = 1 gallon A gallon jug of water = 4 quarts
Worked Example — Chain Conversion

How many cups are in 3 gallons?

3 gallons × 4 = 12 quarts 12 quarts × 2 = 24 pints 24 pints × 2 = 48 cups
COMMON TRAP

The CBEST does not test metric volume (liters, milliliters) — it tests U.S. customary. Do not confuse fluid ounces (volume) with ounces (weight). They share a name but measure completely different things. A fluid ounce of water weighs approximately one ounce, but they are not interchangeable in problems.

(4) Choosing the Right Unit

The CBEST may ask you which unit is most appropriate for measuring something. The key is scale: match the unit to the size of what you are measuring.

LENGTH
Inches: small objects, paper, pencils
Feet/Yards: rooms, fields, fabric
Miles: roads, cities, running distances
WEIGHT
Ounces: food portions, letters
Pounds: people, boxes, produce
Tons: vehicles, shipping cargo
LIQUID VOLUME
Fl oz / Cups: beverages, cooking
Pints/Quarts: dairy, juice containers
Gallons: paint, water jugs, pools

Test Ready Tips — Chapter Summary

U.S. Units of Measurement — At a Glance
Larger → Smaller unit Multiply by the conversion factor
Smaller → Larger unit Divide by the conversion factor
Length chain 12 in = 1 ft | 3 ft = 1 yd | 5,280 ft = 1 mi
Weight chain 16 oz = 1 lb | 2,000 lb = 1 ton
Volume chain 8 fl oz = 1 cup | 2 cups = 1 pt | 2 pt = 1 qt | 4 qt = 1 gal

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