Grammar Hero's ASVAB Math Review: Back to the Basics of Arithmetic Reasoning (Free ASVAB Tutoring)

Introduction

This tutorial provides a comprehensive review of arithmetic reasoning concepts that are essential for the ASVAB exam. Following the steps outlined will help you practice key math skills, such as converting decimals to fractions, performing addition and multiplication, and understanding percents. The aim is to enhance your problem-solving abilities without relying on calculators or reference sheets.

Step 1: Convert a Decimal to a Fraction

• Identify the decimal you need to convert.
• Count the number of decimal places.
• Use the count to create the fraction:
  • For example, 0.75 becomes 75/100, which simplifies to 3/4.
• Practice this by converting different decimals to fractions.

Step 2: Simple Multiplication

• Review the basic multiplication tables.
• Solve multiplication problems by breaking them down:
  • For example, to multiply 6 x 7, think of it as (6 x 5) + (6 x 2).
• Try various multiplication problems for practice.

Step 3: Adding Fractions

• Ensure the fractions have a common denominator.
• If they don’t, find the least common denominator (LCD).
• Convert fractions and then add:
  • Example: 1/4 + 1/2 becomes 1/4 + 2/4 = 3/4.
• Practice with different fractions.

Step 4: Simple Addition

• Add numbers directly.
• For larger numbers, break them into parts:
  • For example, 27 + 45 can be solved as (20 + 40) + (7 + 5).
• Practice with random addition problems.

Step 5: Convert a Fraction to a Decimal

• Divide the numerator by the denominator.
• For example, 3/4 becomes 0.75 when you divide 3 by 4.
• Practice converting various fractions to decimals.

Step 6: Fractions to Decimals

• Use long division if necessary.
• Remember that some fractions may terminate, while others may repeat.
• Continue to practice with different fractions.

Step 7: Understanding Percents

• Remember that percent means per hundred.
• To convert a decimal to a percent, multiply by 100.
• For example, 0.25 becomes 25%.
• Work through examples to solidify this concept.

Step 8: Simple Addition of Decimals

• Line up the decimal points before adding.
• Add as you would with whole numbers, and place the decimal point in the answer directly below.
• Practice with various decimal addition problems.

Step 9: Long Division

• Set up the long division problem correctly.
• Divide, multiply, subtract, and bring down the next digit.
• Repeat until you’ve divided completely.
• Practice with different long division problems.

Step 10: Adding Decimals

• Line up the decimal points.
• Add as you would normally, ensuring to include the decimal point in your final answer.
• Continue practicing with different decimal addition problems.

Step 11: Fractions to Decimals (Again)

• Revisit the conversion process of fractions to decimals.
• Use long division if necessary to practice.
• Ensure understanding of terminating vs repeating decimals.

Step 12: Long Division with Remainders

• Follow the long division steps but keep track of any remainders.
• Express the answer as a whole number with the remainder or as a decimal.
• Practice with problems that include remainders.

Step 13: Subtracting Decimals

• Line up the decimal points.
• Subtract as you do with whole numbers and drop the decimal point straight down.
• Practice various subtraction problems.

Step 14: Comparing Fractions, Decimals, and Percents

• Convert all forms to the same format to compare.
• Determine which is larger or smaller by evaluating their values.
• Use examples for practice.

Step 15: Multiplying Decimals

• Multiply as you would whole numbers.
• Count the total number of decimal places in the numbers being multiplied.
• Place the decimal point in the product accordingly.
• Work through multiplication problems for practice.

Step 16: Rounding

• Identify the place value to which you are rounding.
• Look at the digit to the right to determine if you round up or down.
• Practice rounding various numbers.

Step 17: Understanding Percents Again

• Revisit the concept of percents.
• Practice converting different decimals and fractions into percents.

Step 18: Dividing Fractions

• Invert the divisor (the second fraction) and multiply.
• For example, to divide 1/2 by 1/3, multiply 1/2 by 3/1.
• Practice with different fraction division problems.

Step 19: Comparing Fractions

• Again, convert fractions to a common denominator or to decimals for comparison.
• Identify which is greater or smaller through practice.

Conclusion

This tutorial has walked you through essential arithmetic reasoning topics relevant to the ASVAB exam. Regular practice of these concepts will enhance your math skills and boost your confidence. Remember to pause and work through the examples provided, checking your answers as you go. For further study, consider revisiting challenging areas or practicing with additional resources. Good luck!