SUBTRACTION IN FRACTIONS GRADE 7 - UBRIGHT MINDS ACADEMY

Subtraction of Fractions Notes

Subtraction of Fractions

Just like addition, there are 3 simple steps to subtract fractions:

Make sure the bottom numbers (the denominators) are the same.
Subtract the top numbers (the numerators). Put the answer over the same denominator.
Simplify the fraction (if needed).

Example 1.18:

57 − 27 = 37

Example 1.19: Solve

512 − 13

Solution: Put the fractions under one denominator (12):

512 − 412 = 112

Example 1.20: Evaluate

623 − 156

Solution: Convert to improper fractions:

203 − 116

Put the fractions under a common denominator (6):

406 − 116

Subtract the numerators:

296 = 456

Fraction Game

Score: 0

Fraction Subtraction Exercises (Mixed Fraction Input)

Fraction Subtraction Exercises

`; }); } // Helpers function gcd(a,b){ return b===0?a:gcd(b,a%b);} function lcm(a,b){ return a*b/gcd(a,b);} function improper(whole,num,den){ return whole*den + num; } function toMixed(num,den){ const w = Math.floor(num/den); const n = num%den; return [w,n,den]; } function reduce(num,den){ let g=gcd(Math.abs(num),den); return [num/g,den/g]; } // Parse user input mixed fraction like "4/4/5" function parseMixedInput(str){ const parts=str.split('/'); if(parts.length===3){ const w=Number(parts[0]); const n=Number(parts[1]); const d=Number(parts[2]); return w*d + n; // improper numerator }else if(parts.length===2){ return Number(parts[0]); // assume simple fraction } return NaN; } function check(i){ const ex=exercises[i]; let ans=document.getElementById(`ans${i}`).value.trim(); let ansNum=parseMixedInput(ans); let correctNum, correctDen; if(ex.type==="frac"){ let n1=parseInt(ex.q[0]), d1=parseInt(ex.q[1]); let n2=parseInt(ex.q[3]), d2=parseInt(ex.q[4]); let common=lcm(d1,d2); correctNum = n1*(common/d1) - n2*(common/d2); correctDen = common; }else{ let w1=parseInt(ex.q[0]), n1=parseInt(ex.q[1]), d1=parseInt(ex.q[2]); let w2=parseInt(ex.q[4]), n2=parseInt(ex.q[5]), d2=parseInt(ex.q[6]); let i1=improper(w1,n1,d1), i2=improper(w2,n2,d2); let common=lcm(d1,d2); correctNum = i1*(common/d1) - i2*(common/d2); correctDen = common; } [correctNum, correctDen] = reduce(correctNum, correctDen); let [cw, cn, cd] = toMixed(correctNum, correctDen); // mixed fraction const fb=document.getElementById(`fb${i}`); if(ansNum === correctNum){ fb.textContent=`✅ Correct! Answer: ${cw} ${cn}/${cd}`; fb.className="feedback correct"; }else{ fb.textContent=`❌ Wrong. Correct: ${cw} ${cn}/${cd}`; fb.className="feedback wrong"; } } function showWorking(i){ const ex=exercises[i]; let work='', correctNum, correctDen; if(ex.type==="frac"){ let n1=parseInt(ex.q[0]), d1=parseInt(ex.q[1]); let n2=parseInt(ex.q[3]), d2=parseInt(ex.q[4]); let common=lcm(d1,d2); let n1adj=n1*(common/d1), n2adj=n2*(common/d2); correctNum = n1adj - n2adj; correctDen = common; [correctNum, correctDen] = reduce(correctNum, correctDen); let [cw,cn,cd]=toMixed(correctNum,correctDen); work=`Step 1: LCM of denominators: ${d1}, ${d2} → ${common}
Step 2: Adjust numerators: ${n1}×(${common}/${d1})=${n1adj}, ${n2}×(${common}/${d2})=${n2adj}
Step 3: Subtract: ${n1adj}-${n2adj}=${correctNum}/${correctDen} (simplified)
Step 4: Mixed fraction: ${cw} ${cn}/${cd}`; }else{ let w1=parseInt(ex.q[0]), n1=parseInt(ex.q[1]), d1=parseInt(ex.q[2]); let w2=parseInt(ex.q[4]), n2=parseInt(ex.q[5]), d2=parseInt(ex.q[6]); let i1=improper(w1,n1,d1), i2=improper(w2,n2,d2); let common=lcm(d1,d2); let n1adj=i1*(common/d1), n2adj=i2*(common/d2); correctNum = n1adj - n2adj; correctDen = common; [correctNum, correctDen] = reduce(correctNum, correctDen); let [cw,cn,cd]=toMixed(correctNum,correctDen); work=`Step 1: Convert to improper fractions: ${i1}/${d1} - ${i2}/${d2}
Step 2: LCM: ${common}
Step 3: Adjust numerators: ${n1adj} - ${n2adj}
Step 4: Simplify: ${correctNum}/${correctDen}
Step 5: Mixed fraction: ${cw} ${cn}/${cd}`; } document.getElementById(`work${i}`).innerHTML=work; } displayQuestions();