SAT Fractions and Decimals: Operations, Conversions, and Practical Fluency

Adding and subtracting fractions requires a common denominator: 1/2+1/3=(3/6)+(2/6)=5/6. Multiplying fractions is simpler: (1/2)*(3/4)=3/8 (multiply numerators and denominators). Dividing fractions uses the rule "keep, change, flip": (1/2)/(3/4)=(1/2)*(4/3)=4/6=2/3. Simplifying fractions means reducing to lowest terms: 6/9=2/3 (divide both by GCF of 3). Always simplify final answers. Common mistakes: adding numerators and denominators separately (1/2+1/3≠2/5), or forgetting to find a common denominator before adding. A fraction operation checklist: (1) For addition/subtraction, find the LCD and convert both fractions. (2) For multiplication, multiply straight across (numerators and denominators separately). (3) For division, flip the second fraction and multiply. (4) Simplify the result by dividing both numerator and denominator by their GCF. Practice these operations on 10 problems daily until they feel automatic.

Complex fractions (fractions within fractions) simplify by treating the numerator and denominator as separate expressions, then dividing. (1/2)/(1/3)=(1/2)*(3/1)=3/2. This is faster than simplifying step-by-step.

Converting fractions to decimals: 1/4=0.25 (1 divided by 4). 1/3≈0.333... (repeating decimal, often approximated as 0.33). 1/2=0.5. Converting decimals to fractions: 0.75=75/100=3/4. Converting percentages: 25%=25/100=1/4=0.25. These conversions are useful for mental math and estimation. Memorizing common fraction-decimal-percent equivalents saves time: 1/2=0.5=50%, 1/3≈0.33=33%, 1/4=0.25=25%, 1/5=0.2=20%, 1/10=0.1=10%. A conversion routine: When you encounter a percentage, immediately convert to the fraction form if you know it (20%=1/5, for example). This conversion often simplifies calculations. When you encounter a decimal or fraction in a problem where percentage might be cleaner, convert. Flexibility between forms accelerates mental math.

Three micro-examples: (1) Find 25% of 80. Convert: 25%=1/4, so (1/4)*80=20. (2) Divide 150 by 0.5. Convert: 0.5=1/2, so 150/(1/2)=150*2=300. (3) Compare 2/5 and 40%. Convert: 2/5=40%, so they are equal. These conversions make problems intuitive rather than computational.

Using fractional equivalents for mental math: Instead of computing 18*0.25, think 18*1/4=18/4=4.5. Instead of 50*0.2, think 50*1/5=50/5=10. These mental calculations are faster than decimal multiplication. For division by decimals, convert to fractions: 100/0.5=100/(1/2)=100*2=200. For percentage problems, convert to fractions: 60% of 200=(3/5)*200=120. Mental math with fractions strategy: (1) Convert the decimal or percentage to a simple fraction if possible. (2) Apply the fraction operation (multiply by numerator, divide by denominator). (3) Simplify using factoring and canceling. (4) Compute the final result. This approach avoids decimal arithmetic, which is error-prone, and uses the simpler logic of fractions.

Three micro-examples: (1) 35% of 200=(7/20)*200=7*10=70. (2) Divide 144 by 0.75=(144)/(3/4)=144*4/3=48*4=192. (3) Find 1/6 of 90=90/6=15. These mental calculations accelerate test-solving because you are not using a calculator for routine arithmetic.

A 1-week fractions and decimals drill solidifies fluency. Days 1-2: Practice fraction operations (addition, subtraction, multiplication, division). Days 3: Convert between fractions, decimals, and percentages. Days 4-5: Use mental math with fractions and decimals on computation problems. Days 6-7: Apply these skills to word problems and multi-step questions. Common errors: (1) Adding numerators and denominators when adding fractions (remember: find LCD first). (2) Forgetting to simplify fractions in final answers. (3) Making arithmetic errors in mental math with fractions (double-check by alternative method). (4) Converting percentages incorrectly (remember: 25%=1/4, not 0.25 directly; though 25%=0.25 as a decimal). Track which errors you make and drill those specifically.

On test day, when you encounter a problem involving fractions, decimals, or percentages: (1) Determine whether a conversion would simplify the problem. (2) Convert if helpful (fraction to decimal or vice versa). (3) Perform the operation using mental math if possible (faster and less error-prone). (4) Verify your answer by checking it makes intuitive sense (a percentage of a number should be less than the number, a multiplication of two positive decimals should be smaller than each, etc.). This strategic use of conversions and mental math accelerates problem-solving on the SAT.